Or it means that people who chose to get vaccinated were healthier to begin with. That's called the "healthy vaccinee effect."
And why lookee here. Why, that's exactly what the CDC said it means right there, in the very same study:
The lower mortality risk after COVID-19 vaccination suggests substantial healthy vaccinee effects (i.e., vaccinated persons tend to be healthier than unvaccinated persons) (7,8), which will be explored in future analyses. Mortality rates among Janssen vaccine recipients were not as low as those among mRNA vaccine recipients. This finding might be because of differences in risk factors, such as underlying health status and risk behaviors among recipients of mRNA and Janssen vaccines that might also be associated with mortality risk.
Among persons aged 12–17 years, mortality risk did not differ between Pfizer-BioNTech vaccinees and unvaccinated persons; only 12 deaths occurred in this age group during the study period. The unvaccinated group might be more similar to the vaccinated group in risk factors than are vaccinated and unvaccinated adults.
There is no indication in the study that such an effect exists in the amount shown by the data. In the 18-44 band most deaths are caused by accidents, followed by suicide and homicide.
It looks like the size of the effect reported in the paper can't be explained by healthier people joining the vaccinated group. Logically, wouldn't it be likely that people with health conditions would be more likely to get vaccinated? The CDC paper notes that they have tried to ensure that both groups had equal amounts of use of medical services so one group wasn't unable to obtain medical treatment.
Your theory requires that significantly more people with health conditions who are seeing doctors decided not to get vaccinated. And that people who did get vaccinated are less likely to be the victims of a homicide, or an accident.
Could you enlighten all of us about why that would be?