Meiri says “baruch ba’al hamuznayim”, which I think means that while it was the reason, we cannot question why someone who does something doesn’t get the schar associated with it.
Interesting ohr zarua – implication seems to be that she herself didn’t know the true reason (which is interesting of itself – from the fact that they asked her it seems that Chazal assumed she was able to properly judge which of her actions bring a particular schar).
As to the actual association – O.Z. is saying that an important attribute of the Kohein Gadol was to be a Tahor (clearly) and a Tzanua (?)