For reference, Appalachia defined from the Appalachian Regional Commission, with approximate location of Middletown circled in red:
As his book goes into, he did spend a lot of time in Jackson KY as a kid due to having family in the area. And I have no doubt that it influenced him. But you are correct, it isn't Appalachia and it comes across not genuine at all for him to claim that he hails from there.
On top of this, the thing that bothers me a little bit is that even with his hometown of Middletown, the reality is that he left, went to Ohio State, ended up at Yale Law School, wrote his book and landed in the VC world of the Bay Area. I don't begrudge him for getting out, a lot of people do; I went to college and ended up elsewhere - couldn't do what I do for a living in my hometown. But while growing up in a small town can influence the outlook of people who have left, the reality is that for someone like JD who got the hell out as fast as he could and graduated into the "elite" class, it comes across phony as hell when he claims to have special insight. People recognize it.
There's a longer discussion to be had on how radically his views of where he came from have changed since the time he wrote his book as well - whether one agrees with Kevin Williamson's views, his piece on JD does a really good job of breaking down the discrepencies and is well worth the read.
https://thedispatch.com/article/government-isnt-your-mamaw/