The Appalachians were historically the eastern boundary of the "midwest". Considering that western PA is to the west of the Appalachians, those Pennsylvanians may, in fact, be correct.
I'm from Western PA, and while I wouldn't say I see a lot of people calling themselves midwesterners, we're more alike than we are different. Western PA is hard to classify in terms of region. Most of us just say we're from Pittsburgh/Erie/whatever and leave it at that. But since it is hard to classify, 10% or so of us saying that we're "Midwestern" does not surprise me.
Rust Belt works. Ohio is really part of three different places; the Rust Belt, Appalachia and the Midwest. Maybe The Rust Belt isn't considered polite anymore, I don't know, but my mother's side of my family is entirely from the Pittsburgh to Cleveland area so I mean no offense. My grandfather was a career engineer at Bethlehem Steel, for example. His joke was that he literally sold bridges for a living.
80% of the state is to the west of the Appalachian chain. We haven't been midwestern since Ohio gained statehood in 1803. However, nearly 10% of my state has tied itself to an identity as a Midwesterner because for 20 years conservatives have been calling it "the real america". It's like Pennsylvanias flying the Confederate flag. It's about identity, not history or reality.
Some people consider Pittsburgh to be part of the Midwest for whatever reason. I guess it's because it's a rust belt city that's closer to Cleveland than it is Philly.