Some recent information-hiding schemes are scrutinized in terms of their cryptographic secrecy. The schemes under study appeal to the so-called matrix embedding strategy, designed to optimize embedding capacity under distortion constraints, as opposed to any cryptographic measure. Nonetheless, we establish conditions under which a key equivocation function is optimal, and show that under reasonable key generation models, a perfect secrecy property is nearly satisfied, limited by a mutual information measure that decreases exponentially with the block length