One last detail of some (minor) importance.

By the late 1920s, cow milk was safe and doctors started recommending bottled milk. 

But one doctor found that breast milk was still more protective than cow milk, at least for measles. Makes sense, but not worth studying further for my purpose.

This fact doesn't overturn the main thesis - that protection provided against bacterial infections by ANY FORM OF CLEAN MILK was the main driver of reduction in measles mortality. 

Q.E.D.