Here's a link to the study for everyone else: https://www.nejm.org/doi/full/10.1056/NEJMoa2203965

I did a quick read of the study, and the study is comparing previous infection immunity with vaccination immunity. It does not say anything about being unvaccinated with no prior infection.

TL;DR of the study is 2 dose vaccination is similar or slightly worse than natural immunity through previous covid infection, 3 dose immunity is better, and previous infection + booster is best.

So I would say your claims of being unvaccinated is better is misleading at best. You must be unvaccinated and also have immunity through a previous infection. But again, the study claims higher efficacy to be previously infected and have a booster, so vaccinations are still better.