I have heard many stories about Gedolim where they gave a different reason for the action than the real reason as not to embarass a person.
For example Rav Yaakov Kamenetsky wasnt sure about someones Kashruth on Pesach so he said he didnt each Gebroachs as not to embarass that person.
They story about Rav Moshe could have been the following. Someone could have given him spoiled milk and Rav Moshe did not want to embarasses the person for doing so , so said it was Chalav Stam as they would not be as bad as giving him spoiled milk