I have no idea if R Moshe ever at cholov stam, but as others stated, his whole family did (my dad remembers sharing a Hershey bar with his grandson).
My cousin asked my grandfather, a talmid of R Moshe’s and a good friend of R Reuven’s, and he said that the story sounded like shtus to him.
Jewish Thinker, do you keep asking this in order to prove that there is no source, or because you believe that there is a source out there somewhere and you want to find it? It does seem like there is no readily available credible source, but you won’t be able to prove it. After all, in a world of white sheep, one cannot definitively prove that only white sheep exist, but the sight of only one black sheep can disprove that.