To play devil's advocate with you, I doubt an entire navy ship is seeing false negative across the board. What I was told; her son has never tested positive, but many many on the ship are getting sick again and testing positive for the 2nd time. That is all I know and you can probably rest assured the Navy is not telling anyone the details for publication. Take it for what it is worth.
There is no vaccine for HIV for a reason, the virus mutates. So does covid. That is the bigger take away for me.