This is my rough suggestion based on clinical and research experience. I believe that the only way to avoid incorrect measurement of CTR is to set several rules in place prior to its measurement. In your case, before obtaining the reading for ensure the following:
1) Whether the film is rotated (balance between space between clavicle and sternum on both sides)
2) Inspiratory or expiratory film
3) Use the same device/ruler in the measurement
4) Ruling out kyphosis/scoliosis
Of course you could add more rules than specified above to make your measurement more accurate, even if you feel that there still a silhouette. That would at least speak volumes of the efforts you have taken to avoid bias in your measurements.
Let's say the acquisition was bad and I am left with an image where the heart is actually obscured by a chest condition and there's no way of differentiating because of poor contrast. Is CTR measurement impossible in this case?
In the example you mentioned above, unfortunately, it would be very difficult to determine CTR. Myriad problems with the x-ray film definitely render it a bad idea to determine CTR as it would be grossly inaccurate.
If you still need to determine the CTR regardless, my advice would be as follows:
1) Get the x-ray reported by the radiologist to determine what is the chest condition (?pneumonia, ?sarcoidosis).
2) Based on that report, specify that the CTR values are an 'estimated' one in view of the impediments faced in acquiring a good film
It all depends. If you are doing it for research purposes, I am sure there will be other samples available to you. If it is of clinical relevance, I suggest you proceed with other forms of imaging such as CT thorax to help you out.