I see you are mostly correct. The underlying data is from the CDC. According to them:


"Vaccination status: A fully vaccinated person had SARS-CoV-2 RNA or antigen detected on a respiratory specimen collected ≥14 days after completing the primary series of an FDA-authorized or approved COVID-19 vaccine. An unvaccinated person had SARS-CoV-2 RNA or antigen detected on a respiratory specimen and has not been verified to have received COVID-19 vaccine. Excluded were partially vaccinated people who received at least one FDA-authorized vaccine dose but did not complete a primary series ≥14 days before collection of a specimen where SARS-CoV-2 RNA or antigen was detected.

Deaths: A COVID-19–associated death occurred in a person with a documented COVID-19 diagnosis who died; health department staff reviewed to make a determination using vital records, public health investigation, or other data sources. Rates of COVID-19 deaths by vaccination status are reported based on when the patient was tested for COVID-19, not the date they died. Deaths usually occur up to 30 days after COVID-19 diagnosis."

Seems pretty methodical to me. I think you're correct that there can be variations in the data but not enough to change the outcome. However, I can find no better data.

We can agree to disagree, the study is significantly biased towards the vaccine. Also, there is a data lag that will probably last years, which means that data will be heavily revised in the future. The other problem is that Covid is only a serious disease in people with a dysfunctional immune system, the vaccine does nothing to address this. It reeks of statistical manipulation, time will tell.