Whey is just a small part of milk, though. You can't isolate one aspect and pretend it's fair to call it (cow) milk.
You wouldn't call whey protein powder mixed in water milk.
You wouldn't call butter mixed with water milk.
You wouldn't call casein powder mixed with water milk.
You are correct. Thankfully I never said anything of the sort.
I said proteins, plural. The s is a key indicator I was talking about more than one aspect.
Milk is about 5% lactose, 3.5% casein (80%) and whey proteins (20%, almost entirely two specific sub proteins), and 3-4% fat. A negligible amount of minerals. Nonfat milk, which I think we'd both recognize as milk (unpalatable as it may be). Lactose free milk is milk, I think. One assumes lactose free nonfat milk is milk.
So if one is producing the three primary proteins, you've got nearly the whole way there. There's some trace proteins you are missing, but if you are 99.99+% of the way to milk, you've got milk. You sure the milk you get from the store hasn't denatured those trace proteins?