His conduct was far more detrimental to himself than to the integrity of the game; that is how. Baseball’s gambling policy is posted in every locker room - someone surely must have read it to Charlie Hustle at some point. Players have to sign a statement affirming they know the rule. Assuming Petey put his X on it, he knew exactly what he was doing. Baseball clearly and constantly has made gambling a greater sin than boozing and carousing.
Basically the HOF uses the votes of a bunch of hack sports writers, who are most likely living shall we say morally questionable lives themselves, to judge the games greatest on whether or not they are HOF material.
These athletes are human beings and are subject to the same failings as everyone else and to diminish them based upon those failings,or exalt them until they fail is wrong.