The first thing I would do after testing positive is arrange to take another test.
We're divers here, and most of us are clearly not public health physicians. Let's put this in different terms....
You're on the boat, diving on Punta Sur Cathedral, planned depth of 90'.
Everyone else on the boat analyzes their tanks and gets the expected Nitrox 32, and 0PPM of CO.
You check your tank with the same tester. It reads 38% O2 and it shows 10PPM of CO.
Do you:
[1] dive the tank anyway, figuring that you got a false reading
[2] test again with another analyzer, and dive the same tank if it reads differently with a second analyzer
[3] dive a different tank
If you make a bad choice on this dive, you don't put anyone else at risk.
If you don't like the result of your COVID test and get another test -- maybe that's the right thing to do, getting a more sensitive PCR test. If the two conflict, get a third test as a tie-breaker.
Of course, if the idea is just to walk out with a nice negative test after gargling with mouthwash, you may be putting everyone else who is enclosed on the plane with you at risk, without their knowledge or consent.