I'm looking for a source, though the 25x factor was part of the 29 July 2021 CDC leaked report.
I'm happy to correct / update my comment with a reputable source.
From US CDC:
Reports of death after COVID-19 vaccination are rare. More than 363 million doses of COVID-19 vaccines were administered in the United States from December 14, 2020, through August 23, 2021. During this time, VAERS received 6,968 reports of death (0.0019%) among people who received a COVID-19 vaccine. FDA requires healthcare providers to report any death after COVID-19 vaccination to VAERS, even if itβs unclear whether the vaccine was the cause.
The claim was "Natural immunity comes with a 10--25x greater risk of death". That's a statement about the chance of dying from the vaccine to the chance of dying from Covid.
The numbers you're actually using are something quite different: they're comparing the chance of dying from Covid if vaccinated, vs. the chance of dying from Covid if unvaccinated.
The only credible reports of Covid vaccine fatalities that I'm aware of were from the AZ and J&J ones, and seemed to be on the order of 100 cases in all European countries before the use of those vaccines was stopped at least for the at-risk group (young women).
If the chance of dying from the vaccine was only 10x lower than that of dying from Covid, we'd have millions of dead from the vaccine. We don't.
If we are going with differentiating "all causes" then surely this should be done with infections as well? I don't have numbers on hand but the last CDC report I saw (March 2020 to 2021 I think it was) had only 740 deaths "from [Delta variant of] COVID-19" compared to a few hundred thousand of "all causes" (with COVID). Granted even if those numbers are accurately relayed by my memory (and I doubt they are) the Delta stuff didn't take off until much later, but I'm kinda just making a point here. What that point is I dunno, but I'd just like more apples to apples comparisons in these discussions.
I'm happy to correct / update my comment with a reputable source.
From US CDC:
Reports of death after COVID-19 vaccination are rare. More than 363 million doses of COVID-19 vaccines were administered in the United States from December 14, 2020, through August 23, 2021. During this time, VAERS received 6,968 reports of death (0.0019%) among people who received a COVID-19 vaccine. FDA requires healthcare providers to report any death after COVID-19 vaccination to VAERS, even if itβs unclear whether the vaccine was the cause.
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety/ad...
As of 23 August 2021.
Note that 6,968 deaths is from all causes, not necessarily COVID-19. It's about 100x below the IFR of COVID-19.