They are accurate, your own source says they're accurate. Their only contention is that the figure is misleading on the sole basis that it's the overall rate as opposed to a breakdown by age or vaccination status. So for those vaccinated .08 drops to .02 (or lower). For those over 50 it increases to 1.9. No shocker, risk always increases with age. Still, .08 is an accurate overall rate for those unvaccinated. But, that isn't scary enough so they have to editorialize.
Their hospitalization rate is 1.9 per 100,000, the majority of which being over 85 years old.
Which is inflated because 39% of those patients were in the hospital for reasons not related to Covid and just happened to test positive. I guess it's part of their routine to test all patients.
https://assets.publishing.service.g...393/Weekly_Flu_and_COVID-19_report_w26_v3.pdf
Those are the numbers and I'm sorry but I don't see how your source refutes any of that.
Also:
https://nypost.com/2021/07/08/dont-buy-the-hysteria-the-delta-variant-is-actually-less-dangerous/
The breakdown of age and vaccination status is literally the most important part of understanding risk of serious illness or death from the delta variant. So the information is accurate, but not relevant without that information.
Every hospital in my area are testing every inpatient for covid. We have daily calls to share data. It will vary by hospital system though, but it's a common practice.