I get the impression that the mistakes that bayesians are trying to correct with their after the fact testing of the model are different ones to this one.

If you choose a single model to work with, you are effectively putting zero probability on all other models (that are not contained in your chosen model as sub-models). Gelman's posterior predictive checks aren't motivated by this consideration (one of his non-mainstream-for-a-Bayesian stances is that model probabilities aren't useful). Nevertheless, the checks are directed at identifying ways in which the model fits the data poorly, with an eye to guiding further model elaboration, so they do address this issue in a sense.

"putting zero probability on it"... is a terminal mistake that makes the process distinctly non-bayesian.

Philosophically this is true, but practically speaking, it's not. Setting certain posterior probabilities to zero can be a good approximation to a fully Bayesian analysis (e.g., this paper). In fact, if it's appropriate to use a small number of sigfigs in your results, this approximation can yield the exact same results far faster. I don't think it's fair to call the labeling of such an analysis as Bayesian a lie.