Hm. That seems pretty relevant.
It also matters if (or rather, how much) the false positives correlate. If they are close to being independent samples, then you could take two tests or more tests to increase your confidence.
But if false positive are more likely for asymptomatic people, then the tests must be at least somewhat correlated.
I saw guidelines along the lines of “You can stop self-quarantining if you had two negative tests taken more than 24hrs apart, with first test at least 3 days after an exposure”. I do not know where this came from, but I saw it from an org that I would expect to be fairly sane in making evidence-based decisions.