I agree in principle, and I think this is what's happening mostly. But IMHO the public perception of a paper being peer reviewed as somehow "more trustworthy" is also kind of... bad.
I mean, being peer reviewed is a signal of a paper's quality, but in the hands of an expert in that domain it's not a very valuable signal, because they can just read the paper themselves, and figure out whether it's legit. So instead of having "experts" try to explain a paper and commenting on whether it's peer reviewed or not, I think the better practice is to have said expert say "I read the paper and it's legit", or "I read the paper and it's nonsense".
IMHO the reason they make note of whether it's peer reviewed is because they don't know enough to make the judgement themselves. And the fallback is to trust a couple anonymous reviewers attest to the quality of a paper! If you think of it that way, using this signal to vet the quality of a publication to the lay public isn't really a good idea.
I mean, being peer reviewed is a signal of a paper's quality, but in the hands of an expert in that domain it's not a very valuable signal, because they can just read the paper themselves, and figure out whether it's legit. So instead of having "experts" try to explain a paper and commenting on whether it's peer reviewed or not, I think the better practice is to have said expert say "I read the paper and it's legit", or "I read the paper and it's nonsense".
IMHO the reason they make note of whether it's peer reviewed is because they don't know enough to make the judgement themselves. And the fallback is to trust a couple anonymous reviewers attest to the quality of a paper! If you think of it that way, using this signal to vet the quality of a publication to the lay public isn't really a good idea.