There’s a lot of nonsense written about Reb Moshe’s shita, by people who’ve never cracked a sefer in their lives, and wouldn’t know how to read a teshuvah. Here are the facts:
1. In the machlokes whether Cholov Yisroel is a dovor shebeminyan, i.e. a decree by Chazal that can never be changed, or merely a takono that applied only when there is a real concern for treife milk in the supply, Reb Moshe absolutely and unequivocally sided with the Chasam Sofer, that it is a dovor shebeminyan, and therefore there is no heter to drink milk that is bought, e.g., from a goyishe farm.
2. Having said that, Reb Moshe then goes on to pasken that all commercial milk is cholov yisroel. He is emphatic that this psak is not merely a heter bish’as had’chak, but is 100% his opinion of what the halacha really is. To understand why he holds this you must learn all the teshuvos in Igros Moshe on the topic, not just the short ones. But those who dispute that he held this are simply liars. Stupid liars, because they rely on people not looking inside at the teshuvos.
3. Having said that, and having made it as plain as he could, Reb Moshe then says that it’s a hidur not to rely on his heter. That a baal nefesh should not rely on it, that he himself doesn’t rely on it, and that Jewish schools, which exist for the sole purpose of educatig Jewish children to be mehader bemitzvos, must not rely on his heter. He never says why one should not rely on it, since he repeatedly insists it is the true halacha. Nonetheless, this is what he says.
4. The fact is that although he himself did not drink commercial milk he did allow it in his home, and his Rebbetzin and children did drink it, even though regular cholov yisroel (i.e. not just according to his shita) was available in NYC.