I'm sure the doubt remained. What you wrote kind of reinforces my point that it's very hard to be sure that an expensive mistake was an honest mistake.
Personally, though, I didn't quit to try to double-bluff. I'm a self-preservationist. I'm in the business of keeping myself alive, and I draw the line at working for someone who threatens me.
I'm aware that quitting could've seemed shady, but at that point it was the least of my worries. And I doubt it's the normal course of behavior, either, if someone were caught skimming. Someone who was guilty of malfeasance, who was offered to keep the job, would have almost certainly chosen to stay and lay low while finding some new way to scam them, because that person needs either the money or the frisson. I enjoyed 'em both but I didn't need either enough to risk my life on another accident.
Someone who lacks any trust will always find reasons to assume the worst, as you say. There's a bit of a corollary, though, in my experience, which is: People who choose to continue working around those people also mostly can't be trusted. And I feel like the trust-less parties are well aware of that.
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.
Who said anything about quitting indignantly on principle? The sequence of events goes like this:
1. Dealer deals a round of cards, does not intend to reveal a card, but does anyway.
2. Dealer is informed that if that happens again, he'll be executed.
No amount of indignation is necessary to get the dealer to quit. All that's necessary is that the dealer believe the assurance he's given in step 2. The mistake is guaranteed to happen again -- if the dealer was able to avoid doing it, that's what would have happened in step 1.
In interactions of bluff, bluff, and double bluff suspicion never dies.
Quitting indignantly on principal is either a sure sign of innocence or a true con artist cutting and putting distance from a 'scam', staying can be just as ambiguous.
I'm not doubting your innocence here, just doubting that there was any action you could take that would convince a suspicious mind that you were clean.
I dare say had you stayed then eventually something else would have happened around you down the track (that's just life). Parting ways and moving on saved you from that at least.