We show that there exists a natural protocol problem which has a simple solution in the random-oracle (RO) model and which has no solution in the complexity-theoretic (CT) model, namely the problem of constructing a non-interactive communication protocol secure against adaptive adversaries a.k.a. non-interactive non-committing encryption. This separation between the models is due to the so-called programability of the random oracle. We show this by providing a formulation of the RO model in which the oracle is not programmable, and showing that in this model, there does not exist non-interactive non-committing encryption.