There's Central, and then there's SOUTH Central. People in SC drop the word "South" for shortness; it's implied. Even we would admit that true "just Central" PA is, as you said, State College.

Plus, Harrisburg is the political capital of the state, so in that manner, it's central. With respect, there's nothing up in State College but a big ol' university in a tiny town, mountains and woods. (source: having visited a few times, and my partner is an ex-Nittany Lion.)