An analgous example of how respiratory spread from pathogens can be easily overlooked:

"One of our lab’s major research goals is to figure out how Y. pestis developed its ability to specifically cause pneumonic plague. Our research, recently published in Nature Communications, offers new insights into how small genetic changes fundamentally affected the emergence of Y. pestis as a severe respiratory pathogen.

Prior to our study, the consensus in the field has been that pneumonic plague was a secondary byproduct of the invasive disease associated with bubonic plague. As pneumonic plague represents only 5%–10% of current plague infections in humans, the field has presumed that pneumonic plague occurs only once Y. pestis reaches the lungs following systemic infection, as might occur during bubonic plague. While this may be the case now, it may not necessarily represent what occurred in the past, especially as Y. pestis was just emerging from its ancestor Y. pseudotuberculosis...

This suggests that Y. pestis was first a respiratory pathogen before it was able to efficiently cause invasive infections.This discovery challenges our traditional notion of how plague evolved. Rather than pneumonic plague being a late addition to Y. pestis’s arsenal as commonly believed, its ability to target the lung came before the change that makes it such an infectious pathogen."

(D Zimbler The Conversation June 30 2015)

During background reading, I have just come across this highly relevant article by C Price-Jones An Enquiry into the Causation of Tuberculosis in Children, Practitioner 1903,71:191:

"The question is rightly asked, whether a child is ever infected by the bovine or other varieties of the bacillus contained in the swallowed matters passing through the alimentary tract..

"Death-returns -- with or without autopsies -- have created a large literature on the subject, but have produced much conflict and confusion of results.."

"It was upon the fact of this great rarity of primary intestinal tuberculosis as defined by him, and in spite of the "multitudes" of bovine bacilli swallowed in milk, that Koch based his opinion that bovine tuberculosis was not transferable to man.   Lord Lister.. says...in the case of a child fed on unboiled milk from a cow with a tuberculous udder in a room infected with tubercule, it might be fairly open to question whether the bacilli of bovine tubercule imbibed at its meals, or those of human tubercule derived directly from the inhaled air, were the more numerous in its intestine..

Sir Clifford Allbutt ..."allowed his own family and servants, as well as two other families living near, to consume the highly "bacilliferous" milk of a favourite cow..

"It has been eagerly assumed that ingestion of cows' milk  containing the B.tuberculosis bovis is the cause of the large death-rate from tuberculosis in children. The steps of the argument being that at this age (a) the child is weaned; (b) it is fed on cows' milk; (c) the milk is loaded with bacilli of bovine tuberculosis.  That the majority of children are weaned between the first 9 to 12 months of life is probably true; but the rest of the argument is pure assumption and is probably false.. 

"It does not seem very probable that cows' milk is a frequent cause of tubercular infection in children after they are weaned..

CP-J's own study looked at 55 consecutive postmortems in a children's hospital, 21 with TB. He judged 6 of these to have TB of alimentary origin, just one of these being an infant.  So much for the idea that tuberculous milk was killing infants, all the more so since this 10-month old infant had been "entirely breast-fed"!   A century later and we are none the wiser!

While researching another topic, I have come across this article by GA Allan in Lancet 1913;2:1535:

This was a fatal case of bovine TB in a 12 week infant in Glasgow.  "The infant was really breast-fed...There seems no sufficient grounds for supposing that the (cow's) milk was the direct source of infection."  He quotes no literature to support the notion of TB from cow's milk in infants, but mentions Koplik's (1912) review which concluded that in a great percentage of of cases infection can be traced to a person infected with tuberculosis who had been in the immediate vicinity of the infected child.   Here, the most likely source was the infant's adopted brother who had bovine TB of the neck and mouth. 

In the continued absence of evidence (not presumption) that TB can be got from milk, I have looked at some authors who should know of any such evidence:

1. F Ryan  TB: The Greatest Story Never Told.

"Inhalation is the commonest way in which it gets into our bodies...

The second main way to contract tuberculosis is by drinking milk from an infected cow.  One of the great public health measures which helped in the war against milk-borne tuberculosis was the skin testing of cattle.."

Evidence for this causal link is evidently part of the story never told, since no references were supplied.

2. T Dormandy  The White Death

"Tabes mesenterica...was the form of tuberculosis most commonly caused by the milk-borne bovine strain of the organism...

In 1925 over 8 per cent of milk samples in Dublin contained live tuberculosis bacilli, suggesting that few if any children growing up in the city could escape consuming organisms.."

Comment:  Yet Irish infant mortality rates as a whole were fairly low by European standards at that time.

"Nobody questions the contemporary evidence that...unboiled cow's milk contributes to the potential devastation of gastrointestinal tuberculosis"

Which explains why no one is bothering to document such evidence here.  However, there were dissenting voices in the past (p334), distinguished doctors who said there was no scientific proof that childen acquired tuberculosis from drinking infected milk;  that Guy's hospital took no precautions over tuberculous milk; that milk-sellers had low rates of TB; that small does of TB bacilli in milk might actually benefit infants.

3. H Bynum  Spitting Blood

"Tabes mesenterica...was indeed more common in childhood because children ingested the then unknown bacillus in their milk"

I could find no reference there to back up this statement. 

Edmund Cautley, author of a standard textbook on Infant Feeding, writes:

"The best milk supply for an infant is the mixed milk of a large number of cows, which are healthy in every respect...

Should this Milk be boiled? --The answer to this depends on many circumstances, such as the freshness of the milk, the possibilities of contamination, the fear of tuberculosis...Though personally, I am a little afraid of the spread of tuberculosis from cow to child throught the medium of tuberculous milk, the matter is still sub judice, and at present must be regarded as a possibility."

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Comment:   If anyone should know of definite evidence to this effect, it shoud be him.   Mixing of milk must mean that nearly every infant is exposed to tuberculous bacilli.

Another expert opinion from the time when spread of TB via milk should have been obvious had it occurred (Holt LE Infant Mortality and its Reduction especially in New York City  JAMA 1910;54:682):

"The prevalence of tuberculosis is closely associated with overcrowding and insanitary dwellings. The exciting cause in infants is usually exposure to adult cases of pulmonary tuberculosis...Such close contact usually leads to infection of the infant. To such exposure we have been able to trace definitively nearly one-half of the cases of tuberculosis in infants admitted to the Babies' Hospital in recent years, and it certainly existed in a very much larger number than we were able to demonstrate.. .

It causes 5.6 per cent of the deaths under one year in an institution like the Babies' Hospital...Tuberculosis will not be materially reduced by sterilizing milk, for it is a very small fraction of the patients who acquire the disease in this way"...   

Another doubter of the link between milk and TB:

Gleitsmann JW  Channels of infection in tuberculosis  Ann Otol Rhin Lar 1906;15:819

"Mortality in tuberculosis in Sweden and Norway, where almost all mothers nurse their children, is greater than in Germany.   It is also high in Havana, China, the Philippines, in which countries very little milk is consumed.  The same condition prevails in Japan...How easily erroneous deductions are sometimes drawn from insufficient observations, is shown by the often cited case of Ollivier, in support of milk infection...The cow belonging to the school, when killed, showed extensive tuberculosis, from which a milk infection seemed evident.. But on further investigation it was proven that the milk had always been boiled..." 

At last I have found a study looking at individual factors in infant TB rather than examining collective ones:

Mathews P On the Etiology of Tuberculosis in Infancy and Childhood  Brit J Child Dis 1906;3:96-110

This is based on 25 cases of TB with clinical histories and post mortems. Taking first the 9 cases dying in infancy,

• 8 had been breastfed (? higher rate than normal for the general [Newcastle] population)
• Only one had had any cow's milk at all, but had also been breastfed for one month by a mother with TB
• Only one child had not been breastfed, an illegitimate child fed throughout on patent foods

There were 4 more cases aged 1y.  These had been breastfed for an average of 13 months, and none were reported to have been fed on cow's milk.  In only two of these cases was it known that the parents did not have TB.

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Conclusion

Even though numbers were small, TB spread by cow's milk in infants can be discounted.  In any case, there are also more plausible alternative explanations available for spread of TB.