In this paper we consider the problem of reversible information hiding in the case when the attacker uses only discrete memoryless channels (DMC), the decoder knows only the class of channels, but not the DMC chosen by the attacker, the attacker knows the information-hiding strategy, probability distributions of all random variables, but not the side information. We introduce the notion of reversible information hiding Incapacity, which expresses the dependence of the information hiding rate on the error probability exponent E and the distortion levels for the information hider, for the attacker and for the host data approximation. The random coding bound for reversible information hiding B-capacity is found. We obtain the lower bound for reversibility information hiding capacity for E rarr 0. In particular, we have analyzed two special cases of the general problem formulation, pure reversibility and pure message communications.