When playing the boolean game (δ,f), two players, upon reception of respective inputs x and y, must respectively output a and b satisfying δ(a, b)=f(x, y), in absence of any communication. It is known that, for δ(a, b)=a ⊕ b, the ability for the players to use entangled quantum bits (qbits) helps. In this paper, we show that, for δ different from the exclusive-or operator, quantum correlations do not help. This result is an invitation to revisit the theory of distributed checking, a.k.a. distributed verification, currently sticked to the usage of decision functions δ based on the AND-operator, hence potentially preventing us from using the potential benefit of quantum effects.