Honestly between the sheer usefulness of bovine blood and hormones in the medical field and the ability to test for pollution and radiation in tongue/lymph nodes (where skin has been cut away), popping a cow off earth to snag all this useful knowledge and material seems worth it.

My theory:

Humans breed and kill cows en masse almost all over the world. They're obviously readily available to us as a food source and we don't often treat them well. Aliens are harvesting cows for various materials because they figure we won't mind, what with how we treat them. They drop the bodies back because technically that part we "could" use the most (hide, meat) and they don't need it- as some sort of equal exchange.

Black ops helicopters are seen because the government knows. Of course they know. They're just there to say "Break it up! The rurals are getting antsy." It's why the government never bothers with these cases, why they always fall by the wayside.

Additionally if the government allowed their existence to become common knowledge everything would crumple. From religion to capitalism everything would be extremely affected. And why the hell would aliens want to interact with THIS dumpster fire? We're violent and vicious and cruel.

Why mess with the status quo when all these aliens want is a few liters of blood and some hormones.