I've read Jaynes (I used to spend long hours trying to explain to a true-believer why I thought MaxEnt was a bad approach to out-of-equilibrium thermo), but my point is that for small sample data, assumptions will (of course) matter. For our frequentist, this means that the experimental specification will lead to small changes in confidence intervals. For the Bayesian this means that the choice of the prior will lead to small changes in credible intervals.

Neither is wrong, and neither is "the one true path"- they are different, equally useful approaches to the same problem.