Some of these people would have perhaps died from the common cold. When you are aged and infirm particularly with conditions that compromise your immunity, it doesn't take much to send you over the rainbow.
For the very same reason we've overcounted COVID deaths, we're likely to overcount COVID deaths of the vaccinated. As they say, some of these people have one foot in the ground and the other on a banana peel.
Your general point is correct, but that is exactly the reason that medicine traditionally recommended against vaccinating old and frail people...anything could be the “last straw”.
These days they just want to jab anyone who can’t fight back—without regard for consequences.