Is there some misunderstanding in English that “biased” means “factually false”? I’ve seen a lot of people on the internet confuse them as the same thing.

Bias is supposed to mean something that is factual but presenting a one-sided opinion by e.g using a subset of facts and language meant to influence the readers opinion.

Nothing whatsoever - they are technically correct (the best kind of correct). And yet it is also a descriptor that is likely to prime the reader with a negative connotation. There's a reason that witness oaths require not only "nothing but the truth", but first of all "the whole truth".

I read it as acknowledging a preconception the reader is likely to have and therefor building rapport with the reader, not necessarily a sign of bias by the author.

That just sounds like bias with extra steps. Which subset of readers is the author choosing to build rapport with? Which subset are they choosing not to build rapport with? Why one, and not the other? And anyway, why build rapport at all - this isn't an opinion piece.