Worse, "VAD affects immune response and predisposes the host to infection, and infection decreases the intestinal absorption of the VA, thereby contributing to secondary VAD development."

IF YOU ALREADY HAVE VITAMIN A DEFICIENCY - AND GET AN INFECTION, THEN YOU CAN'T ABSORB VITAMIN A FROM THE INTESTINE. 

This is probably what explains the failure of Vitamin A supplementation AFTER an infection (as found in some studies).

It is necessary to take it BEFORE any infectious exposure.Overall, I'd give around 80% chance that the MILK hypothesis adequately explains the measles mystery. 

There might be something else involved, as well - but for now I'm done with this question and will document it, and write a summary for my Times of India blog. 

Btw, if anyone objects to my explanation, please let me know - and also any alternative hypothesis.