Sounds like communism. No cause can be considered greater than freedom.
> No matter what you argue beyond, the epidemiological aspect is now not really the point here anymore. He faked stuff
He should be investigated for faking then and expelled/imprisoned/fined by a court if evidence proves him guilty.
> second test was just created so he counts as recovered, which was the requirement to get in if not vaccinated
Just test him antibodies/T-cells + PCR and you know if a person used to be sick and recovered. No necessity for speculation here. Presence of immunity (which one only get through overcoming the sickness or a vaccine) is an objective thing. Is it not?
I would also suggest introducing a law sentencing people who falsely claim they are immune or expose others to a risk of being infected any other way to serve a sentence aiding in a hospital taking care of infected people.