Here is the Chazon Ish. He is clearly saying that government supervision is good according to the Pri Chodosh.
R’ Moshe’s heter is that we have an anan sahadi, so it actually has a din of cholov Yisroel, whereas the heter on butter is that it’s not required to be cholov Yisroel.
The comparison to butter might work for the Pri Chodosh/Chazon Ish, but not for R’ Moshe.
I’ll try to find the source referring to kashering.