The cited study explicitly compares previously infected (not vaccinated) individuals to vaccinated individuals, so your claim is wrong. However I will say, in

The cited study explicitly compares previously infected (not vaccinated) individuals to vaccinated individuals, so your claim is wrong. However I will say, in a lot of the CDC literature they inconsistently refer to "unvaccinated" individuals in a manner that often does not distinguish between those with prior infection and those who are immunologically naive. I think this has been a major point of confusion for the general public who are trying to interpret the results of such studies.