home game controversy needs settling

[brb9h]

16 person home-game tournament is down to 5 players. First 3 players fold to the blinds. SB goes all-in with QQ. BB (slightly smaller stack than SB) thinks for a long time and finally calls with A7o.

The players turn their cards face up, and after everyone sees what they have, the BB notes that the dealer (one of the other three remaining players) absentmindedly shuffled the folded cards back into the deck. BB says that it's a misdeal, and that the hand should start over. SB says that because the hands were already face up, the dealer should deal the cards out despite the improperly shuffled-in cards.

Who is right?