First responders get you to the hospital, hopefully alive. They don't diagnose. They don't fill out the death certificate. Also, people that are rushed to hospitals in an ambulance will very likely get an autopsy, and thus the cause of death will be delayed for several weeks while the autopsy results are processed.
I can speak from first hand experience that Utah is likely under counting COVID deaths significantly. The state is currently not performing post-mortem covid-19 tests. So, unless you got a test before you died you won't be counted. Now, this could change with the updated CDC guidelines. But that is where we are at as of now.
This just isn't true. Period.