Being vaccinated doesn't just entail having had covid and flu jabs within two years.
And being unvaccinated doesn't just entail not having had covid jabs and having had flu jabs within two years.
So therefore it's not a raw comparison of unvaxxed and vaxxed.
It does not tell you the unvaxxed vs vaxxed data
Say in a hypothetical world, as a clear example, to get vaccinated you had to have a chip inside your arm to track you (made up)
Now the CDC study above controls for chips
vaxxed and unvaxxed must have the chips
but it ASSUMEs the chip wont have any effect on the results