You are correct, but that doesn't mean it's anecdotal. At this point we don't know whether natural immunity is 'better' than vaccine induced immunity, and it could go either way. There are many disease (including viral ones!) for which the vaccines are orders of magnitude more effective [1].
The simple reason being that the vaccines have the spike protein as a marker - the part of the virus that we expect is least likely to change significantly.
What we do know is that the current Delta variant, which is a fitness escape but also partly an immune escape, has infected a number of people that had the vanilla variant.
> You are correct, but that doesn't mean it's anecdotal. At this point we don't know whether natural immunity is 'better' than vaccine induced immunity, and it could go either way.
There is this study: https://www.nature.com/articles/s41591-021-01377-8 saying that natural immunity seems to be slightly worse than Pfizer or Moderna vaccine, but better than AstraZeneca or Johnson vaccine.
