To be fair, this is also illogical, at least in a literal sense. It’s the Appeal to Authority fallacy. The reputation of the speaker doesn’t necessarily confirm or deny an assertion they make.

Granted, most people tend to use some combination of both logic and heuristics in practice to determine their own understanding of the truth, perceived reputation being a fairly common one.

> To be fair, this is also illogical, at least in a literal sense

Mostly in the same sense as arguments from induction are "illogical". Appeal to authority is essentially an inductive argument, and those are just as logical. Of course, they deal in probabilities rather than certainty, unlike deduction, but that doesn't make them illogical.

It does make it illogical, in the same way that “dealing in probabilities” makes many other things illogical. Like, for example, crime statistics.

All of physics, and science in general, is based on arguments from induction. If you want to call that illogical too, then, fair enough.

Sure, but so is listening to doctors(' websites). That's why there's a LOT of checks and balances around who gets to claim to be a doctor !