Are vaccinations better than natural immunity? Common sense would say no, but headlines like "Unvaccinated People Are Twice As Likely To Face COVID-19 Reinfection" seem to indicate they are. Suspiciously, the articles don't actually draw that conclusion, but they don't discourage it either. That should trigger your spidey sense.
The actual paper is here. People who contracted COVID in 2020 and did not vaccinate were compared to people who contracted COVID in 2020 and did vaccinate in 2021. The first group were over twice as likely to get reinfected. This should not be surprising. Both kinds of immunity wear off over time and the vaccine was more recent. For previously infected people, the vaccine is essentially a booster shot - unnecessary, because death and serious effects are extremely rare after either kind of immunity. Once you have had the disease or a vaccination, COVID is simply another common cold.
The media believes vaccination of previously infected people is a good thing, and they will embrace a paper that can mislead people into doing so, without regard to factual accuracy.