Well, does the (flimsy) reasoning break down if the cow is fed corn instead? Corn is still a vegetable.

Even adding animal-based products like bone meal should be fine, since the bones are made out of processed vegetables.

Now you are thinking like a politician!

Of course. A school cafeteria would never give students subpar food.

I mean, Zea mays is panicoideae, and thus very much a grass..