Read the teshuva. you can make up this “3rd category” all you want.
OK, I will list the three categories. Please tell me which one you disagree with:
1) Cholov Akum: milked without supervision, without any external reasons, such as govenment regulations or remoteness from any b’heimah t’meiah, to think there’s no milk from a b’heima t’meiah mixed in. Assur.
2) Cholov Yisroel: milked under proper supervision. Muttar.
3) Cholov HaCompanies/Cholov Stam: milked without specific supervision, but subject to government regulation. Some say assur, Rav Moshe and others say muttar, Rav Moshe says baal nefesh yachmir, apushatayid will opt for category 2 instead, when possible.
If course I’ve read the teshuvos. He doesn’t quite use my wording, but all three categories are alluded to.