Eliezer,
I like your essays, but I feel that you are really beating a naive and unsophisticated frequentist straw man (straw person, politically correctly speaking). I think that the answer to the question “Should we draw different conclusions?” depends on some further assumptions about the process and about the type of conclusions we want to make. What kind of frequentist would think that his research is free of subjective assumptions? A naive one.
I admit that I am out of my depth and I would like to know more about Jaynes example.
Erratum: in the comment above, it should say “his or her research” ;)