It is hard to say that the title of this article is correct, at least based on this CDC publication.
This is a case Control Study with a few challenges. The background does not mention cohort studies already performed in this area (the cohort studies which already exist are a higher level of evidence than this type of case-control investigation), but instead incorrectly states "few real world epidemiologic studies exist to support the benefit of vaccination for previously infected individuals." They should have cited NEJM Dec 23 regarding those with COVID antibodies, and SIREN study in Lancet comparing natural immunity with vaccination, both of which address the potential protective effect of recovery from previous infection.  Does not provide number of total cases from which cases and controls were selected.  Reader should beware that odds ratios, often used in case-control studies, may exaggerate a difference between groups. The background infers that the authors intend to show "the benefit of vaccination for previously infected persons."  This article does not show the benefit of vaccination in previously infected individuals, since they did not include a comparison group of previously infected patients who were also vaccinated.  Note: what is really needed is more meaningful outcome studies, with endpoints that matter, such as hospitalization, endotracheal intubation and mortality.