I just don't agree with that. People are bound to have different opinions on a subject such as this. If they can find that he didn't bet against the Reds, there is absolutely no reason to not allow him into the Hall of Fame. Even though that will be extremely difficult to determine, if it is proven he never bet against his team that doesn't challenge his integrity to the game and to the Reds while playing. Which also shouldn't exclude his name from HOF balloting and should have his name removed from the ineligible list.
I truly believe that he didn't bet against the Reds because of the way that he played. Obviously, some of the ways and natures of things that he did on the field while playing aren't custom things that other players were doing at the time, and that can be one indication that the guy cared so much about his team, that he wouldn't bet against them. He had an extra motivation to drive him to help his team win.
That's obvious to me simply identified by the way he played the game. He played it with an undeniable integrity to help the Reds win every game with motivation.