Chalav Stam is not trief like Pigs Milk
That’s true. Chalav stam is a machlokes, and at worst is an issur d’rabbonon. Pig’s milk is an issur d’Oraisa.
BTW I think on of the reasons regular Milk is ok, is because its not Chalav Akum, but rather Chalov Machine.
I dont think even in Chalav Yisroel does a jew milk the cow, Its probably the same machine in the same dairy farm (Likely a special run where someone just watches the process).
The issur has nothing to do with who does the milking, as long as there’s no supervision, it’s assur (aside from the heterim which may apply in our times in the U.S.)