For starters, let's clear up any confusion concerning this payoff. In Three Card Poker, straights beat flushes. They also pay more on the optional Pair Plus bet-5-1 or 6-1 for a straight vs. 3-1 or 4-1 for a flush, depending on the schedule in use. In this situation the player must have been playing the Pair Plus wager. (An excellent aid for playing this game is the James Grosjean Three Card Poker/Let It Ride strategy card.)
It's important to keep in mind that in human-dealt games, mistakes are inevitable. For that reason the casino adds layers of backup where possible. On a crap table, for example, a big part of the boxman's job is to make sure that payoffs are made correctly. In a game like Three Card Poker, however, it's not practical to have more than one person on a game. Instead, pit personnel are there to be called in to rule on a dispute over a botched payoff.
In this case, the dealer caught his mistake and pointed it out to you, which is standard procedure, especially when another hand has not yet been dealt. When this happens, if the player agrees, the remedy can be made right there and the game goes on. If the player disagrees, or simply doesn't understand, a floorman will be called in to mediate. After the situation has been explained to the floorman, there are usually procedures in place by which cards can be backed up (pulled out of the discards to recreate the hand) to help resolve the dispute. If the amount at issue is small, you can often get a ruling in your favor. But if it's large, and both sides stand firm, then surveillance may be brought in, and as a last resort, Gaming Control.
In your case it sounds as though you didn't know if the dealer was right or wrong, but went along with it. That's not a bad thing. The dealer likely wouldn't have asked for the correction if he wasn't fairly certain that the mistake had been made. And if there were other players at the table, that's a further safeguard, as players tend to chime in when they see something happening that isn't Kosher. Bottom line: Correcting mistakes on a game is normal, the way it was done here seems standard, and you probably weren't taken advantage of in any way.
An important point to keep in mind is that catching mistakes is a two-way street. Dealers often make errors in the house's favor that it's up to you to bring to their attention. In these cases, even when the dealer agrees with you, a floorperson will almost always be called in to oversee the correction.
