Non-Burned card

[PantsOnFire]

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I think this (re: PantsOnFire) would be standard when I've seen it happen in casinos. Of course it doesn't matter which card is which since they're random, but some people are very attached to the idea of a specific card being the one they "deserved" to get.

If there were significant action I think you'd have to let it stand, but I'm not sure what the definition is. I think it's two players acting.

If someone who missed the flop folded to a bet, then you can't very well rule their hand dead yet change the flop, can you?

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You are correct that action changes everything. That's why an experienced player at the table should point this sort of thing out right away.

And as far as the "deserved" card aspect etc., well it does work both ways. A player may like the second and third card and feel the first (burn) card should be removed and the next (fourth) card flopped.

That is exactly why I advocate following the rules exactly in these situations. Although, as you pointed out, if the first two guys take action before the mistake is caught, then that's a clear rule as well to continue with the action. (Can't remember how to handle the turn).