Your entire scenario has almost nothing to do with tarnishing the game and is a better explanation of how it tarnishes betting.
Of course it tarnishes the game. If Pete bets every day but one, on the day he doesn't bet he could be doing something to try and throw the game to help ensure a loss (just cause Pete says he didn't throw games doesn't make it true, he has lied about everything.) Even if he isn't trying to throw games....that's the message it sends!!He brings a cloud of doubt over the games because of his gambling. Are the games now legit? Or being thrown? It tarnishes the games!! That is the message it sends to the people he gambles with and to anyone who knows he gambles in general. It tarnishes the game. Because now those people take this info and go bet against the Reds with the info...."hey Pete isn't betting on the Reds tonight, Pete bets on the Reds all the time, something is up, hey lets go bet against the Reds." Now some random game in May on a Tuesday has an unusual ton of money bet on it as word spreads through the gambling world. MLB doesn't want that. It makes the games look fishy and fixed. Or...if Pete is in the hole for however much money he has lost, instead of paying the money back he doesn't bet on a random game when he is always betting, ...it could be info to the bookie that hey Pete is telling us something here (in reality Pete probably just told them bet against us we never beat this pitcher), let's just call his debts square if what we think is gonna happen tonight happens. Now he is providing information to bookies and gamblers that tarnishes the game and brings a cloud of doubt over the game.
That's why Players can't bet on baseball. Who you bet for to win is not the point and is meaningless. By betting you bring a cloud of doubt the game is on the up and up. It turns games into Pro Wrestling! Even if you don't bet for one day you are sending a message. Not to mention Pete has LIED about everything from day 1. Every time new info comes out...its Pete caught in a lie. So when Pete says he never "threw a game"....who the hell can believe him at this point. He probably did! He gambled as a player, as a manager...both things he said he never did. Pete is a liar. He probably did tank and try to throw games. All the evidence points in that direction.