what we do is simply calculate P(E|~H) (techniques for doing this being of course the principal concern of statistics texts),

No no no. That would be a hundred times saner than frequentism. What you actually do is take the real data e-12 and put it into a giant bin E that also contains e-1, e-3, and whatever else you can make up a plausible excuse to include or exclude, and then you calculate P(E|~H). This is one of the key points of flexibility that enables frequentists to get whatever answer they like, the other being the choice of control variables in multivariate analyses.

See e.g. this part of the article:

The authors used what's called a Mann-Whitney U test, which, in simplified terms, aims to determine if two sets of data come from different distributions. The essential thing to know about this test is that it doesn't depend on the actual data except insofar as those data determine the ranks of the data points when the two data sets are combined. That is, it throws away most of the data, in the sense that data sets that generate the same ranking are equivalent under the test.