Sure. But you also need to take into account:
Died, and vaccination status unknown = unvaccinated.
Died, and only received one shot = unvaccinated.
Died, and only received two shots = unvaccinated.
Died, and received the approved arsenal of shots - but died not within the magic time window (e.g., too soon after the shot, or too long after the shot) = unvaccinated.
The CDC and FDA have already shown themselves to be liars throughout this CoVid fiasco, so their claims are meaningless.
True. If you only have two options, vaccinated or not, you need to draw the line somewhere.