I don't know if this is due to an intentional simplification of your examples

Yes, it is. Lawyers and judges have a tendency to invent dozens of fuzzily overlapping concepts without even considering whether one or two concepts could do just as much useful intellectual work. I could tease out the difference between testimonial and nontestimonial evidence, assertions and non-assertions, matters offered for the truth of the matter asserted, matters offered for other purposes, matters pretextually offered for other purposes, matters honestly offered for other purposes but with an unacceptable tendency to prejudice the jury...but I'm not writing a law review article; I'm writing a Less Wrong post. I tried to focus on what I thought the audience would find relevant.

What interests me here is the distinction between the truth of evidence (does the content of this document describe reality?) and the reliability of evidence (would we ordinarily expect documents like this one to describe reality?). Anything further would be an explanation of the law for its own sake.

Davis v. Washington, is not a case about hearsay; just look at the wikipedia summary. The "indicia of reliability test" was abandoned in Crawford.

Give me a little credit, here; don't you think I looked at the Wikipedia summary before publishing the post? I also linked to Michigan v. Bryant, a newer Supreme Court case which extensively discusses Crawford. I think the cases I linked to provide a discussion of evidentiary reliability that illustrates some important Bayesian concerns. Whether every doctrine in every case I cite is still good law is not really the point.

Hearsay, in the vast majority of circumstances, does not involve any kind of balancing test or similar determination.

I may not have been clear on this point -- I'm not claiming that judges weigh evidence to see if it should be considered hearsay. Rather, the very process of determining whether evidence is hearsay appears to be designed so as to indirectly prompt judges to weigh whether evidence is reliable. By systematically applying the rules about what counts as hearsay, judges consciously or unconsciously wind up admitting only evidence that the system views as reliable. If you like, we could say that the people who write the laws of evidence in the first place are the ones who perform the actual balancing test.