that specifically revolves around the infected. Paul is clearly arguing that infection leads to natural immunity, and there isn't any science to date that suggests said immunity goes away (therefore needing the vaccine). Here is a better snapshot of his argument:
https://www.nbcnews.com/politics/politics-news/rand-paul-says-he-won-t-get-covid-vaccine-n1268268
The CDC study doesn't prove Paul needs the vaccine. It's almost making the argument that everybody should both get the vaccine and covid.