Regarding the baseball HOF.... they are a non profit with their own board of directors. I just checked and it does include Mandred, Reinsdorf, Art Moreno, and a handful of former players like Ripken, Griffey, Ozzie, and BIggio. But also business leaders.
I"m sure they are governed by a set of bylaws that can't be deviated from so anything regarding Pete's election to the HOF would go through the normal channels, meaning he has to be voted onto a ballot then voted again for unduction. That means 24 out of 32 people have to agree to put him in. (12 of 16 on each). That is a tall order.