Nisht,
Daas is exactly right. Here is a quote from the teshuva you cited:
???? ???? ????? ?? ????? ???”? ???? ????? ????? ?? ????? ?? ?????? ?????? ????? ????? ???? ?????.
People use the term “chalav stam” as an easy way of differentiating between those milks that a have a cholov yisrael label. But anyone relying on R’Moshe to drink ordinary milk from the supermarket, holds that such milk has the status of cholov yisrael even without the label.