I suspect you're talking past one another, but maybe I'm missing something. I skimmed the paper you linked and intend to come back to it in a few weeks, when I am less busy, but based on skimming, I would expect the frequentist to say something like, "You're showing me a finite collection of 95% confidence intervals for which it is not the case that 95% of them cover the truth, but the claim is that in the long run, 95% of them will cover the truth. And the claim about the long run is a mathematical fact."
I can see having worries that this doesn't tell us anything about how confidence intervals perform in the short run. But that doesn't invalidate the point Wasserman is making, does it? (Serious question: I'm not sure I understand your point, but I would like to.)
Well, I'll put it this way - if we take as our null hypothesis 'these 95% CIs really did have 95% coverage', would the observed coverage-rate have p<0.05? If it did, would you or him resort to 'No True Scotsman' again?
(A hint as to the answer: just a few non-coverages drive the null down to extremely low levels - think about multiplying 0.05 by 0.05...)
http://xkcd.com/1132/
Is this a fair representation of frequentists versus bayesians? I feel like every time the topic comes up, 'Bayesian statistics' is an applause light for me, and I'm not sure why I'm supposed to be applauding.