This question refers to two people with matchplay coupons good at the same casino who use them on opposite bets, such as pass and don't pass on the crap table, red and black or odd and even at roulette, or player and banker at baccarat.
The answer is some casinos do and some don't. There's a little section on this in the coupon chapter of More Frugal Gambling by Jean Scott. She says that most players are reluctant to try this move, because it's embarrassing when a boss pulls them up. On the other hand, plenty of "aggressive couponing couples," including Angela Sparks, Jean's daughter the Frugal Princess, matter-of-factly play their coupons against each other. If they're told they can't, they don't. If no one says anything, they've locked in one sure win (except at roulette where the green 0 and 00 show up on occasion).
It would be impossible to determine which casinos do and don't, especially since it's often up to the particular boss in the pit at the time. If you're bold, try it and see what happens. If you're not, don't.