Does Qur'an 16:66 say milk comes from a cow's stomach?

Qur'an 16:66 states: > And indeed, for you in grazing livestock is a lesson. We give you drink from what is in their **bellies** - between excretion and blood - pure milk, palatable to drinkers. Scientifically speaking, I believe the cow does not produce the milk in its stomach, unless I'm wrong.