That may be but it's not necessarily how the covid deaths stats are collected. I believe in the UK for instance, the definition of a covid death is a death that occurred within 28 days of a positive test, irrespective of the cause of death.

There's not one way to collect these stats, see the section "ONS and PHE COVID-19 deaths data are produced in different ways and have different purposes:" in [0] on what the UK gathers how. Neither of which changes the excess deaths resulting from the pandemic.

It's just a matter of timeliness in some cases and up to the consumer of such data to decide which is suitable for which analysis (and honestly a moot point, no country tests enough to warrant the assumption that the odd accidental death that is later corrected would be worse than the effects of undercounting).

[0] https://www.ons.gov.uk/aboutus/transparencyandgovernance/fre...