this cannot be evidence against B *unless* you have background knowledge on the fraction of people who think B,

No. The "unless" clause is still incorrect. We can know a great deal about the fraction of people who think B, and it still cannot serve even as meta-evidence for or against B.

There is an ongoing confusion here about the difference between evidence and meta-evidence. It is as obvious and important as the difference between experimental analysis and meta-analysis, and it is NOT being acknowledged.