Edit: Ugh, thanks David, I just realised I made a dumbass error calculating the percentages. You’re right. It should be around 1% overall. I’ve corrected the article. It’s worth pointing out that this still needs to be contextualised by age though. The rate drops to 0.6% for under 65s and 0.002% for under 18s (I double checked the numbers this time😅). So when we’re considering risk and policy, it seems very important to include this context.
I only linked to one study but I did look at a number of them before claiming that natural immunity offers better protection than vaccination. I do see the argument for saying "may" or "seems to" though. The reason I expressed it with more confidence is that this is how immunity works for pretty much every disease, and that, at least in my searching, the consensus seems to be that natural immunity offers greater protection because it doesn't rely solely on the spike protein for targeting (the CDC study you linked to was 10 times smaller than the Israeli study that first claimed natural immunity was more protective) .
But the second isn't my claim. It's a CDC estimate (link to the data is in the article). So you're welcome to disagree with the figure, but you'd have to take it up with them. I think they have access to better information than either of us and aren't motivated to underestimate.
In this case, slightly counterintuitively, an estimate is far more likely to be accurate than simply taking deaths and dividing by reported cases. Because what we absolutely know for certain is that cases are underreported. Somewhere between 30 and 50 percent of COVID infects are asymptomatic. So these people wouldn't even think to get tested. There have also been numerous reports of false negatives in rapid tests. Many others simply don't have access to tests or wouldn't have bothered to pay to get one.
We also know that deaths are overreported, because even after two years we're still dealing with this died with COVID instead of died of COVID nonsense. I think this one especially has done a lot of damage to peoples faith in the data.
So a strong statistical model that estimates morality rates will almost certainly be more accurate than reported figures. This is one of many errors that the media simply hasn't attempted to contextualise, either because they're not thinking clearly or because bigger numbers are scarier and get more clicks.