Death WITH Covid and Death WITH Vaccine

Is "death WITH Covid" really "Covid death"? 

 In March of 2020 the Office of National Statistics announced that deaths would be reported differently from then on. No reason for the changes was given, it was simply stated that the changes were happening. The difference was that (a) anyone at all who died after"testing positive" for Covid-19 would be recorded as a 'Covid death" and (b) anyone who died and (in somebody's opinion) might have had Covid-19 before dying would be recorded as 'Covid death'. 

Many commentators, myself included, pointed out this could only exaggerate the Covid problem and make Coronavirus seem much more dangerous____________________________