I'm sure the tens of deaths that happened like this really changed the statistics in a meaningful manner.

The point is that until it's well-defined, we don't actually know, so people will wiggle in doubt if they want to.

Poor definitions enable people to present the data differently depending on their biases and agendas. We should want to prevent that not by grounds of "you're crazy," but by making the definitions non-interpretable.

Does that come up a lot? How many people are currently in hospice in the state of Illinois with a few weeks to live?

There have been a lot of excess deaths in 2020. It seems reasonable to guess those people died of either COVID-19 or our response to COVID-19 (eg reluctance to seek medical treatment). None of these mortality statistics are perfect, but given the fairly short window of a mild COVID-19 infection, it seems pretty reasonable as a first approximation to assume that if they had it when they died, they died from it. There might be some cases where this is wrong (died of severe trauma during a car wreck in which they were a passenger rather than a driver) or questionable (the hospice case) but how much do those really affect the overall numbers?

Illinois averages 300 deaths per day from all causes, so if 3%-5% of all Illinoisians are COVID+, that error starts to add up.

Meh. The excess deaths are a lot more than 3%–5%. In a super quick search: "From Feb. 2 through July 25, Illinois had officially recorded 10,252 more deaths than typically would be expected" [1] => 59 per day. If 300 people died per day (your stat) and 5% of those were misattributed to COVID-19 because they were tested and happened to have a harmless COVID-19 infection (this is a silly upper bound), that's only 15 misattributed out of the 59, so at least 75% are correct. That's already good enough to use for setting policy IMHO. In reality, I doubt everyone who died was even tested, so I think more error lies in the other direction.

[1] https://www.chicagotribune.com/coronavirus/ct-dataviz-corona...

It's pretty hard for to decide how to interpret that, because it sounds like the guy is arguing that the statistics about Covid deaths are really bad and their way of registering a Covid death is completely stupid and therefore it is silly to think there is as bad a situation around the pandemic as you might otherwise suppose - on the other hand the guy who is telling me this is the "Director of Illinois Department of Public Health " and as such most likely responsible for the completely stupid way of registering the Covid deaths.