Num 16:3 And they gathered themselves together against Moses and against Aaron, and said unto them, Ye take too much upon you, seeing all the congregation are holy, every one of them, and the LORD is among them: wherefore then lift ye up yourselves above the congregation of the LORD?
He arose against them BOTH. And Korah himself was a priest - He was of the tribe of Levi... If anything the relationship between Korah and Aaron was a priest challenging the High Priest. And his relationship to Moses was a priest challenging a prophet.
You showed my point well thanks.