State of Colorado was sued in mid-2020 after a guy in a sparsely populated county died of alcohol poisoning (0.55%!!!) and the next day covid count there went up by one. They had to seperate out died with covid. The deaths by covid went down about 23%.
Recently Alameda County, CA & Santa Clara County, CA both both separated out “with covid”. Alameda death count down 25%, Santa Clara down 22%.