The medical examiners actually looked at the patients and put covid on those 3700 death certificates. Likely most of them died in their home before getting a test.
I'm sure it's not 100% accurate, but you wanna know how they come up with our official flu death stats?
"CDC uses a mathematical model to estimate the numbers of influenza illnesses, medical visits, hospitalizations, and deaths in the United States"
https://www.cdc.gov/flu/about/burden...-estimates.htm
I would think it's at LEAST as accurate as flu deaths.