The chart shows that vaccine breakthrough hospitalizations increased a short time after vaccinations began (and became significantly more likely than reinfection hospitalizations), while reinfection hospitalizations among the unvaccinated never increased significantly and were actually lower at the end of the time period. This shows stronger/longer-lasting immunity from infection than from vaccination. At the starting point of the chart, vaccinations had only been around for about 5 months (even less for most age groups), while infections had been rampant for over 15 months.
Vaccines began the end of 2020. In the US they were widely in use by February (vulnerable and old) and everyone by April. This chart starts while they were still getting through the initial vaccines of the general population.
It does not distinguish between mRNA and the J&J vaccine. All studies we have seen show the J&J is not great at prevent infection, and only pretty good at preventing hospitalizations. And it fades much, much faster. There is no way to tell from this data if any of the infections after vaccination are J&J.
It also does not delineate actual populations in the groups. They are estimates: "Whereas vaccinated cohorts were directly observed in the immunization information system databases, unvaccinated persons without a previous COVID-19 diagnosis
were defined using U.S. Census population estimates minus persons partially or fully vaccinated by December 11, 2021, and unvaccinated persons with a previous laboratory-confirmed infection before May 30, 2021."
When you are talking about such low numbers for never infected + vaxxed, infected + not vaxxed, or infected + vaxxed, using census population estimates instead of actual numbers are prone to over-generalizations and wider confidence intervals. When you look at the 95% CI for those groups, most of them overlap. The difference between 0.3 in one and 0.5 in another are statistical noise for many of these samples.
As for Sen. Paul, he doesn't say vaccinations are unnecessary. He says they are unnecessary for those like him who have already been infected. And that is supported by the data from the CDC. But I guess science is only science if it fits the desired narrative.
Like Mori said, he was infected nearly 2 years ago. There is no peer reviewed studies I have seen that show a previous infection prior to Delta or Omincron or AB.2 helps lessen the chance of becoming infected/spreading COVID 2 years later.