But neither of the conditions in the EU pass says you don't have covid now. Vaccinations are not 100% (numbers go down to 70%, and a lot of infections for vaccinated people are asymptomatic, so even worse, because you don't stay at home, and noone tests you), PCR tests don't guarantee you didnt catch it between the test and "now", and having covid 5.5 months ago, does not guarantee you don't have it now.
But they increase the likelihood by a lot. There can't be a perfect system (apart from no one crosses the border, which is not feasible for other reasons), so this is a pretty good compromise.
