What they might have meant is that many countries accept a positive PCR from >= 4 weeks ago as proof of prior infection (and therefore, presumed immunity), but not an antibody test. I'm not familiar with the error rates of the latter, but for the purposes of travel a positive antibody test is rather useless.

Where I live, you need to meet one of three conditions for things like indoor dining:

- proof of a full course of vaccination (2 weeks after the final shot)

- proof of prior infection - antibody test not accepted, only positive PCR between 1 and 6 months ago

- proof of an antigen test (rapid test) that's at most 24h old