Have you read the limitations of this study?
"
[...] some patients classified as vaccinated and previously uninfected might also have been infected."
Another thing is, we all know that covid tests aren't 100% accurate, they could be both false positive or false negative - I have no idea why the authors of this study haven't taken this into account and haven't even mentioned this as one of the limitations (imho a very significant one).
The uncertanity of the tests implicates two things:
- in case of a false positive result in the past, such person was mistakenly identified as the one having natural immunity (unvaccinated group)
- in case of a false negative result (and if vaccinated) such person was added to vaccinated, non previously infected group
There was 5,1% of positive covid tests in vaccinated group and 8,7% in unvaccinated group. Considering all the limitations (also the one the I mentioned but was not included by the authors), I don't think that's a super credible study and the headlines based on it saying "vaccination induced immunity is 5 times better than the natural one" are very misleading.