Died "with" Covid....

[Olive]

I agree.  And I think there are privacy constraints on the reporting of details of deaths.  

Is that a nice way of saying the family of unvaxxed deceased don't want to admit it?

No.   I think are general privacy considerations around reporting causes of deaths, and that includes Covid-19.   And not all families would be ashamed of having unvaccinated members - a few are rabidly anti-vax and would be ashamed of having a vaccinated family member.