Daniel Rosen: I do not understand what you are saying.See The Rambam who says we go by Chazaka ,and a Kohen with a chazaka is a kohen .See the Aruch Hashulchan who says that a chazaka makes a kohen certainly. The site brings Rav Emden but the Chasam Sofer argues on that I believe. The Sdei chemed says that a kohen today is a kohen. See the Rama in Yoreh Deah who also says chazaka.
The final point is that Rav Moshe you are sourcing is in a case of of people who cant be trusted and the chazka is lost,but in no way does it mean a regular kasher kohanic family is not m,yuchus.