The data is coming from the same source, so it's not independent.

No. The FBI's UCR system gets their data from law enforcement organizations.

The CDC's NVDRS links data from coroner/medical examiners, toxicology, and death certificates.

If you did, you would know that 2022 had a huge drop in reporting due to the FBI reducing the number of different systems that local LE could use to upload data to them.

You realize that 2023 isn't 2022, right?

And I note that that your information is out of date.

Second, the FBI decided to accept information in the old reporting format where necessary. As a result, the 2022 annual report now includes data from more than 85 percent of agencies (70.4 percent using the new system and 12.9 percent using the old system), covering 93.5 percent of the population.

but even if it is legit, much of that fall is probably return to the mean following the 2020 spike.

No, that would have happened in 2021. A 13% reduction from 2022 to 2023 would only be regression to the mean if there was a spike in 2022.

a long history of fudging their numbers.

So long as the history is long, the estimate of the trend is still good.

everyone acknowledges that police shootings are under-reported.

So long is they're consistently under-reported, the FBI statistics are still good for estimating the trend.