The CDC study doesn’t control for behavioral differences between the two studied populations, though, which weakens their conjecture that there is a clear causal relationship that confers more immunity to those who’ve had Covid+vaccine compared to those having had just Covid. It seems entirely plausible that people who’ve refrained from getting vaccinated after having Covid are probably not especially careful about their exposure, which can lead to higher rates of infection.

One could just as easily suggest the opposite: that people who have gotten the vaccine, feeling even safer, will engage in more risk-taking behavior because they have the added safety.

With the absence of evidence in either direction, it is unwise to draw either conclusion.

I didn't say anything about the methodology of this CDC study or the study that this comment section is attached to, only that they both say the same thing. They both say that getting the Pfizer vaccine after infection confers additional protection against reinfection. There is no disagreement between these studies' conclusions.

An alternate conclusion to your own is that people who get the vaccine did so in order to take advantage of the reduced restrictions on vaccinated people at the time.