First, I wouldn't call any theory by Caramazza (or Mahon, for that matter, but I can speak to the former's view far more than the latter) in terms of any "mixed proposals that language comprehension is both perceptual and statistical. Yes, I know that in their abstract they specifically call refer to their proposal as a "middle ground", but even within that paper it is fairly clear that the "middle ground" is more between what they describe as a "parody of the disembodied cognition hypothesis" (a sort of "straw man" argument) and a pretty fundamentally disembodied, amodal hypothesis. That sensory-motor systems are required to connect instantiations of a concept to the abstract concept itself not even Plato would deny (that originator of the most extreme version of amodal conceptual representation and categorization in which physical instantiations of an abstract concept refer to an ontological, ideal referent- the "form/idea").

Second - and maybe this is simply me needing to better acquaint myself with the various uses of terms like "statistical learning", "implicit learning", "perceptual learning", "artificial grammar learning", etc.- it seems to me that this isn't just old news but a haphazard conflation of an already over-differentiated area of study (learning and memory; see e.g., the attached). An early version of statistical learning applied phonetics may be found in e.g., Dewey's Relative Frequency of English Speech Sounds and by 1948 we have Shannon's groundbreaking work on communications & information theory already applying statistical learning (albeit more in the computer science/computational intelligence sense) to language. Saffran (cited in the paper you mention and a key figure here) himself explicitly points out that this isn't a novel discovery but a re-discovery:

"While the idea that surface distributional patterns point to pertinent linguistic structures holds a distinguished place in linguistic history (e.g., Bloomfield, 1933; Harris, 1951), statistical learning has only recently reemerged as a potential contributing force in language acquisition (though see Maratsos & Chalkley, 1980). This renewed interest in statistical learning has been fueled by developments in computational modeling, the widespread availability of large corpora of child-directed speech, and empirical research demonstrating that humans can perform statistical language learning tasks in laboratory experiments (e.g., Cartwright & Brent, 1997; Elman, Bates, Karmiloff-Smith, Parisi, & Plunkett, 1996; Gómez & Gerken, 1999; Goodsitt, Morgan, & Kuhl, 1993; MacWhinney, 1999; Mintz, Newport, & Bever, 1995; Redington, Chater, & Finch, 1998; Saffran, 2001; Saffran, Aslin, & Newport, 1996a; Saffran, Newport, & Aslin, 1996b; Seidenberg, 1997; Seidenberg & MacDonald, 1999)"

Saffran, J. R. (2002). Constraints on statistical language learning. Journal of Memory and Language, 47(1), 172-196.

Third, a central reason (unmentioned) for this renewal was because of Chomsky. There were two rival contemporary models for language when Chomsky was first developing most of modern linguistics via the TGG program: the behaviorist account by Skinner which Chomsky famously eradicated in one, fell swoop and the statistical approach proposed by Shannon. More recently (2011), Chomsky again addressed the statistical approach and this time pointed out that even the little work he had produced on statistical learning turned out to be wrong (according to him):

“it's true there's been a lot of work on um trying to apply uh statistical uh models to various linguistic problems…I think there have been some successes, but a lot of failures…The simplest case maybe is…the problem of uh identifying words in a running discourse,  something apparently children do, you know, they hear a running discourse, they pick out units,  and the obvious units are words, which are really phonological units...and it was taken for granted that…if you have a series of sounds and you look at the transitional probabilities uh at each point, what's likely to come next, uh when you get to a word boundary the probabilities go way down…if it's internal to a word, you can predict pretty well,  so if you kind of trace transitional probabilities you ought to get something like word boundaries…I wrote about it in 1955. And I assumed that that's correct. Turns out to be false….

On the other hand there's a lot work which tries to do sophisticated statistical analysis, you know bayesian and so on and so forth, without any concern for the uh actual structure of language, as far as I'm aware uh that only achieves success in a very odd sense of success." (http://languagelog.ldc.upenn.edu/myl/PinkerChomskyMIT.html).

Fourth, and most importantly, both groups in the study rely on perception. The difference between perceptual learning and statistical is half theoretical, half by definition, and somewhere in this intersection are the interpretations of the empirical evidence. However I don't think one can find evidence for an amodal representation of concepts an against embodied cognition by a distinction between statistical learning by perception and "perceptual learning".

A few additional references for your consideration:

Maye, J., Weiss, D. J., & Aslin, R. N. (2008). Statistical phonetic learning in infants: Facilitation and feature generalization. Developmental Science, 11(1), 122-134.

Keidel, J. L., Jenison, R. L., Kluender, K. R., & Seidenberg, M. S. (2007). Does grammar constrain statistical learning? Commentary on Bonatti, Pena, Nespor, and Mehler (2005). Psychological Science, 18(10), 922-923.

ten Cate, C., & Okanoya, K. Revisiting the syntactic abilities of non-human animals: natural vocalizations and artificial grammar learning. Philosophical Transactions of the Royal Society B: Biological Sciences, 367(1598), 1984-1994.

Thank you so much to both of you. Andrew, I take note of your great feedback and cautions. I was aware that I could be over-stretching the link there —now I am quite certain! Very useful references, too. 

Regards