As noted above, all state schools vary in their governance structure and their amount of autonomy and financial support from their state. There’s no one single cookie cutter set up for what constitutes a “state” school. But PSU clearly is a state school.
Also as noted above, PSU may be exempt from SOME legal requirements (like the cited open records laws) because those laws specifically say that they don’t apply to government related state schools like PSU. For other purposes (like application of the federal First Amendment) PSU is treated 100% as a part of the state government.
But under any reasonable definition, PSU is a state school – tuition discounts to in-state students, “State” in its name, employees participating in the PA SERS system, governor and legislature having seats on the board or nominating rights, hundreds of millions of dollars of state appropriations going to the school, etc. etc. etc. I have not studied Cornell’s hybrid set up in detail, but a graduate of any other Ivy League school will derisively tell you in a heart beat that of course Cornell is in fact just a state school.
The main difference appears to be that ALL of Penn State is a state school, while only certain parts of Cornell operate as a state school. NYS residents get a tuition break if they enroll in Cornell’s statutory Ag School, but they pay full freight if the enroll in endowed A&S. Cornell is a pretty unique hybrid as a private/public school. Penn State is one of the pretty typical flavors of high autonomy state schools. Study a few other state flagships and you’ll see that PSU’s position is really not all that special.
Plenty of state schools operate just like PSU does. And some state schools are way more independent than PSU. For example, the law and business schools at UMich and UVA, which are “state” schools that are “financially self-sufficient.” They are way more private than PSU is.
This tedious discussion is kind of like arguing over whether a “charter” school is public or not. Of course charters are public. But charters have a different governance and financial structure that is different from your regular school district school.
PSU is a charter school – public but with a particular legal/financial set up. You can say the same thing about almost any state U.