It's easy to find the paper (it's even linked below), and they of course do attempt to correct for many covariates including geographic locations and socioeconomic effects.
One thing I'd want to check is the difference across time zone boundaries. There's not much of a difference between western Georgia and eastern Alabama, other than time zones; do they have different health outcomes? (Or, if you want to say that maybe Georgia has more money than Alabama for public health, look at a state like Tennessee or Kentucky where the time zone boundary isn't the state boundary.
https://nypost.com/2019/04/23/living-on-the-wrong-side-of-a-...
You can see there are huge cultural differences in a couple of places that could account for all of it. I agree, checking the local difference is a decent way to falsify this stinker. Bootstrapping a few states in and out of the data set would do so also.