Cleveland Clinic study did not go that far. The study looked at 1,300 health care workers who were infected but did not get vaccinated over a period of 5 months and compared them to the general workforce of @52k Clevelan Clinic employees. None of the 1300 infected but unvaccinated workers contracted COVID during the 5 months. The study's conclusions were meant as guidance for vaccination priority in places where there are shortages. To that extent, the study recommends prioritizing unexposed over exposed. But the study did not go as far as to say it is not necessary for exposed people to get the vaccine:
"What we don't know is what's the duration of that protection? And also remember our population of health care workers is younger in general, it's healthier. We're not saying don't get the vaccine," says Dr. Steve Gordon of Cleveland Clinic, one of the authors of the study.
Immune responses from the mRNA vaccines have been observed to be superior to natural infection. So, if there is ample vaccine supply and you want to crush COVID, people with prior infection should still get the vaccine.