This seems to be a crucial disagreement, so we should settle it first.

All right.

you trust Sam to be a good judge and an honest reporter of truth. This means, among other things, that you and Sam share a great many beliefs

Sure, if Sam and I freely interact and I consider him a good judge and honest reporter of truth, I will over time come to believe many of the things Sam believes.

Also, to the extent that I also consider myself a good judge of truth (which has to be nontrivial for me to trust my judgment of Sam in the first place), many of the beliefs I come to on observing the world will also be beliefs Sam comes to on observing the world, even if we don't interact freely enough for him to convince me of his belief. This is a little trickier, because not all reasons for belief are fungible... I might have reasons for believing myself a good judge of whether Sam is a good judge of truth without having reasons for believing myself a good judge of truth more generally. But I'm willing to go along with it for now.

Agreed so far.

you think Sam makes judgements roughly in the same ways you do.

No, I don't follow this at all. I might think Sam comes to the same conclusions that I would given the same data, but it does not follow in the least that he uses the same process to get there. That said, I'm not sure this matters to your argument.

So, you mostly understand the kinds of inferences Sam draws

Yes, both in the sense that I can mostly predict the inferences Sam will draw from given data, and in the sense that any arbitrarily-selected inference that Sam draws is very likely to be one that I can draw myself.

you mostly understand the beliefs that Sam has

Yes, in the same ways.

If you infer from this that B is true because Sam says that it is, you must be assuming that B isn't so odd belief that Sam has no competence in assessing it.

Something like this, yes. It is implicit in this example that I trust Sam to recognize if B is outside his competence to evaluate and report that fact if true, so it follows from his not having reported that that I'm confident it isn't true.

you've got a lot of beliefs about what B is, without knowing the specifics.

Certainly. In addition to all of that stuff, I also have the belief that B can be written down on a slip of paper, with all that that implies.

Essentially, your inference that B is true because Sam says that it is, is the belief that though you don't know what B says specifically, B is very likely to either be one of your beliefs already or something that follows straightforwardly from some of your beliefs.

Statistically speaking, yes: given an arbitrarily selected B1 for which Sam would report "B1 is true," the prior probability that I already know B1 is high.

But this is of course in no sense guaranteed. For example, B might be "I'm wearing purple socks," in response to which Sam checks the color of your socks, and subsequently reports to me that B is true. In this case I don't in fact know what color socks you are wearing.

In other words, if you have good reason to think B is true, you immediately good reason to think you know something about the content of B (i.e. that it is or follows from one of your own beliefs).

Again, statistically speaking, sure.

Thinking that B is probably true just is believing you know something about B.

No. You are jumping from "X is reliable evidence of Y" to "X just is Y" without justification.

If X smells good, I have reason to believe that X tastes good, because most things that smell good also taste good. But it is quite possible for me to both smell and taste X and conclude "X smells good and tastes bad." If "thinking that X smells good just is believing that X tastes good" were true, I would at that point also believe "X tastes good and tastes bad," which is not in fact what happens. Therefore I conclude that "thinking that X smells good just is believing that X tastes good" is false.

Similarly, if Sam reports B as true, I have good reason to think B is probably true, and I also have good reason to think I know something important about the content of B (e.g., that it is or follows from one of my own beliefs), because most things that Sam would report as true I also know something important about the contents of (e.g., ibid). But it's quite possible for Sam to report B as true without me knowing anything important about the content of B. I similarly conclude that "thinking that B is probably true just is believing [I] know something [important] about B" is false.

In case it matters, not only is it possible for me to believe B is true when I don't in fact know the content of B (e.g., B is "Abrooks' socks are purple" and Sam checks your socks and tells me "B is true" when I neither know what B says nor know that Abrooks' socks are purple), it's also possible for me to have good reason to believe that I don't know the content of B in this situation (e.g., if Sam further tells me "Dave, you don't know the content of B"... which in fact I don't, and Sam has good reason to believe I don't.)