That is correct. I tried to allude to that in the end when I said how a Bayesian mysteriously gives a certain confidence to the space of models. In the case of a uniform prior I believe my example is correct.

Usually when Bayesian probability is explained, it often comes across as "duh, that's what anyone would do" except not rigorously with equations. I tried to give an example contrasting a Frequentist and Bayesian approach.