There are two ways to determine the effect of an intervention: controlled experiments and natural experiment.

I'm relying on the natural experiment of CLEAN MILK and associated rapid decline in mortality for diarrheal and measles mortality to deduce the MILK HYPOTHESIS. 

It appears this idea was widely considered in the medical profession for a number of years and they tried to supplement with Vitamin A, with mixed results. But the idea was dropped after antibiotics came to the scene.

Later, it was revived and by now there's conclusive evidence for Vitamin A playing a positive role in defending against measles-caused pneumonia.

It is likely that Thomas McKeown missed drawing this link because these Vitamin A studies had faded into the background by his time.

Anyway, by now I believe the VITAMIN A (MILK) theory can be productively used to explain the MEASLES MYSTERY.