> If you say “ta yiwei X” it means “s/he thinks X” with a strong connotation that X is in fact false.

I was interested to learn just now that Chinese dictionaries don't bother to mention this. I assume the reason is that the analogous construction in Classical Chinese has no such implication.

By contrast, Chinese-English dictionaries vary from noting that 以为 "usually" refers to mistaken belief to outright defining it that way.