Surely it's not proof at all... It's obviously ridiculously easy to fake one, either the test itself or the reporting of it (not saying that would be right btw).
Given that those who aren't vaccinated, in the main, aren't especially concerned about the virus and either believe it's nonsense or massively overblown, aren't they exactly the type who would be much more likely to fake a LFT result rather than miss out on a big event?