It's also possible that the manager just didn't care whether you were guilty or not. By quitting and not coming back, you removed yourself from the equation, and so it's immaterial whether you were trustworthy or not.

There could be nothing more at play here than rational self-interest. You quit to preserve your life; this is rationally the best move for your risk-adjusted interests. The house gets to say (possibly very visibly - did you quit on the spot?) that the dealer no longer works here, which mollifies the customer, because the potentially-corrupt dealer is no longer in a position where they can influence outcomes. So it's the best outcome for the house. And then the hand has already been played, so the customer now has a sunk cost on their bluff, but you're gone, so at least they know that if you are corrupt, you won't be dealing any more hands to them. So it's the best outcome for the customer.

You don't need to trust people who aren't in a position to hurt you anyway. That's why walking away is sometimes so powerful: you just change a bad situation by removing yourself from the equation, and start over somewhere better.