I'm sure that same answer is used to validate the "Hail Mary full of grace" seed of the whole Marian doctrine thing. Such "evidence" has never really materialized though I've read many RC apologetics that try to support Marianism.
And, by the way, the verse is in no way sufficient in itself. There is no support that anything that the Lord may have given to Peter at that time survived Peter.
Wrong. Read the books and educate yourself. I did, and that's part of the reason I'm no longer Protestant. There's lots of evidence--but Protestants choose to simply ignore it.
And I say again---many Protestant positions have been justified with flimsier Biblical backing.