I am mildly interested in the status of the dealer in the hand. Is he folded or does he have a live hand?
It is imperative that the dealer with a live hand never gets to "decide" which board gets the first card any time during the hand. We don't know that the dealer got to see the card before it was placed, but it wouldn't be very hard for that to happen. A few tenths of a second would be enough advance notice in many cases to decide "good card" vs "bad card". The dealer wouldn't even have to have improper intent - dreaming of a heart, sees one as he peels off the first turn card and plops it down as needed all without thinking "I'll take advantage of the situation".
Host needs to keep a careful eye on the table(s) playing circus games. The variety of games can boggle the minds of many players, much less the guy acting as the dealer for this particular hand.
I think the turn is a done deal and not subject to revision. I am not swayed by guidelines for how many actions it takes - two or three or more. Once the betting round is over, that street stays. The river error must be corrected. Objections were raised and there is no reason not to rectify the mistake. "We did it otherwise the prior street" is not a reason to do it wrong on the next street too.
I would not kill the hand. Host must make every effort not to allow situations to arise that allows any dealer (much less one with an interest in the hand) to make a mistake that kills the hand. The potential for abuse, while perhaps unlikely, is a great threat to the game should it come to pass. There are special cases where there isn't a better alternative to killing the hand - fouled deck, cheating, two or more decks making up part of the board, etc. - but those ought to be ultra rare events.
DrStrange