Ok. If a Bayesian picks among a set of models, then it is true that (s)he assumes the disjunctive model is true.. (that is the set of densities that came from either H0 or H1 or H2 or ...) but I suppose any procedure for "drawing conclusions from data" must assume something like that.

I don't think there is a substantial difference between how Bayesians and frequentists deal with induction, so in that sense I am biting the bullet you mention. The real difference is frequentists make universally quantified statements, and Bayesians make statements about functions of the posterior.