No, I think it's fair to say that if someone dies for whatever reason and they test positive for COVID-19 then their death should be included in the official total.
You think that someone who has COVID-19 asymptomatically, and dies from being crushed by a falling piano should be included in the official death total?
If you applied the same logic to prostate cancer, probably 50%+ of men "die" of prostate cancer.
The coroner is supposed to make these judgements, and it’s not entirely clear how you should aggregate them into a big-number statistic. If you go by official cause of death, nobody dies of a cold in most countries. If you go by a positive test, loads of people do.
Bear in mind what we want here is not some absolute, objective truth which cannot exist anyway - as pointed out in other comments, where do you draw the line with this stuff? If someone is 90 and dies after having tested positive, did they die of a new preventable disease or was it just their time? The distinction can end up being arbitrary.
What people care about is numbers comparable with other diseases so the strength of response can be correctly calibrated. And clearly these numbers are useless for that, especially as flu isn't tracked or reported in the same way.
If someone tests positive to the flu but also have cancer, should be considered a flu victim?