Plenty of people said they already had COVID, and they are still in the 10X more likely to die statistics. Either they are had something else (like a flu or a cold, you wouldn't know without a test), or something about natural immunity isn't working. I won't speculate, I believe its the former (easier to confirm that you got the vaccine then if you really got COVID).
People who have had Covid are at least as well-protected against serious illness as anyone who is vaccinated, and probably more so given the latest variants:
> During October 3–16, compared with hospitalization rates among unvaccinated persons without a previous COVID-19 diagnosis, hospitalization rates were 19.8-fold lower (95% CI = 18.2–21.4) among vaccinated persons without a previous COVID-19 diagnosis, 55.3-fold lower (95% CI = 27.3–83.3) among unvaccinated persons with a previous COVID-19 diagnosis, and 57.5-fold lower (95% CI = 29.2–85.8) among vaccinated persons with a previous COVID-19 diagnosis.
Or are you saying a lot of people think they've gotten covid but actually got something else?
If it's the latter case, how do you feel about encouraging that the people who don't want to be vaccinated because they've had a prior infection get an antibody test, and get vaccinated if it comes back negative, and if they do indeed have antibodies we treat them the same way we'd treat someone vaccinated?
If you think that natural immunity is comparable to vaccine-generated immunity, but that proposal still sounds unappealing to you, I'd be curious why.
It's far more nuanced than that. I have now had three doses of the vaccine, and I had Covid subsequent to the third dose. Israel is now moving on a fourth dose, and the vaccine manufacturers are making an Omicron-specific variant. If my city continues with prior behavior, and mandates a booster for a virus I've now had, am I an "anti-vaxxer" for not wanting the unnecessary dose?
That you're characterizing the situation in this binary way says a lot to how the entire issue has been treated as a cartoon political issue. But many millions of people are in exactly this situation, today (i.e. those who already had Covid, and are now being required to get a vaccine).