Iceland accepts either vaccine or previous infection certificates[1][2]. They seemed to handle covid well, being fairly strict.
Fake vaccinations[3], including fake certificates are popular, especially when they are forced. If you want a fake vaccination, I know a guy who knows a guy. Point is - it's not bullshit.
Yes, checking certificates is easier than testing for antibodies. While harder, I still think antibody tests would have less false positives and I most certainly don't think the relative easiness to administer vaccines is a good reason to require everyone to take them, even when they are more immune then those who only got the vaccine.
A friend had an antibody test as he already had covid and didn't want to go for a vaccine. It was no big deal.
[1] https://www.covid.is/sub-categories/travel-to-and-within-ice...
[2] https://www.landlaeknir.is/um-embaettid/greinar/grein/item43...
[3] https://text.npr.org/1026863219