Apushata-
It certainly does matter. As with all P’sak stories, we need to know the entire case with every minute detail to really know what exactly Rav Moshe paskened.
Please see Aruch Hashulchan YD (117:29) that if any soap is Nifsal m’Achilas Kelev, it is permitted according to all. It is no diff than Chametz on Pesach.
Rav Moshe generally Paskened according to the Aruch haShulchan (even over the M”B).