REMINDER: CFR is a proportion, based on the disease's progress in the various infected individuals. If you infect 1000 or 100 80 year-olds, the proportion that die is going to be the same (given the same medical care). The number of deaths will be differ of course.
CFR is also age dependent. In terms of age of population & the expected CFR per age decade, I will remind you these are the CFRs for various countries, based on the countries' demographics & the age-based CFR's (not Infection Fatality Rate, but based on confirmed cases) out of
this study
China: 1.22%, India 0.73%, Italy 2.47%, South Korea 1.71%, Spain 2.16%, UK 1.96%, US 1.73%.
(Personally, I think that study has low numbers, but is getting toward the right ballpark.)
Higher or lower actual measured rates may be due to worse/better care. Surveillance & isolation won't impact the rate (except as lack of those measures may lead to worse care). Widespread testing may lower the measured rates
IF there were a significant ratio of asymptomatic cases found that are then added to the denominator. Conversely, lack of testing may increase the measured rates, if symptomatic cases are not confirmed by testing.
New York and L.A. County have indicated they will not test (some) cases that are expected to be COVID-19. Those jurisdiction's numbers should be considered incomplete & thus wrong. Someone in China might point to their numbers and say they are lying.
As for Chinese stats, I expect that, as in any chaotic circumstance, there were deaths early on from COVID-19 that were not counted. But, by late January, their numbers are probably more accurate than Santa Clara County's. Imagine if our grocery stores required a temperature check before you could enter. if you have a fever, you were taken to a fever clinic, where you were tested. If the test is positive, you are taken from the clinic to the hospital. So, from the time you tried to buy groceries, you had no contact with family (nor did you in the hospital). You had no chance to slip out of the system. They offered monetary rewards for turning people in. I've seen a video of police forcing their way into an apartment of an elderly man who was suspected of being sick. I've seen a video of a group of allegedly sick people tied together by rope being led down the street. I've seen a video of a family being told that their door would be chained shut to keep them isolated (had they been sick, they would have been hospitalized, so I believe this family was simply exposed), and if a fire broke out, they were to call for someone to come unchain them. I've seen a video of what happened when someone with a fever tried to run a roadblock. (I do NOT know that these videos are typical events. I can imagine some of these scenarios happening in the US.)
I would not want to live in such an authoritarian state. But, I think China had the power to institute strict controls that resulted in tighter rein on the spread of COVID-19. The politicians didn't have to worry about an election, or where campaign financing would come from. Could they be lying about their numbers? Sure. But they've been posting their daily numbers since February 13, which have been self consistent. Researchers have apparently gained access to case data from the hospitals and published studies based on those numbers.