In that case it would actually make sense to designate the patients on the low end of the cost spectrum as Covid patients to get the higher bundled reimbursement and to designate the highest cost patients as non-Covid if they can do so so they can unbundle the billing. Interesting.
You want to go down the rabbit hole of medical billing, be my guest. But it's not a helpful topic to the discussion of CoViD numbers IMO.
As I said before, they're not mutually exclusive. There can be many deaths classified as COVID that aren't as well as many deaths that are COVID that aren't included. Another possibility is people are dying from unrelated illnesses due to the lower standard of care, for example the ban on transporting a patient without a pulse. They always do, my grandfathers death certificate says he died from pancreatic cancer. If there is one thing we are certain he didn't have it's pancreatic cancer, but it looks better for them because they "diagnosed" it 10 months prior but no matter what they did they couldn't get it to show up on a biopsy even with a team of the top pathologists in Sloan Kettering because they were barking up the wrong tree. That doesn't change the fact that there are many "COVID deaths" that really aren't COVID.
The point is you can't just point to the money in order to say they're doing it dishonestly and it's because of the money. There are legitimate reasons for the money to be higher for CoViD cases, and it's not necessarily making the hospital more money because the higher billable amount should accompany a higher cost of care. In your example, you have specific reasons to show on the medical side of things where they might have been wrong, and even there it doesn't automatically mean it was a money thing (hubris is a problem too).
Bottom line is that excess deaths is the best metric you're going to get. That's true with or without any discussion of funny business in diagnosing, because not every case can be diagnosed. It's true that there are other factors contributing to the excess deaths number, but it's unreasonable to assume those factors play a bigger role than CoViD itself. There are so many causes of death that see significant downturns in a lockdown scenario - why assume those are smaller than your increase due to lockdown (or other factors).
