According to the Cleveland County Assessor’s office, the City of Norman owns the corner of the section where the park is, the part of the section to the southeast from it is owned by an individual, and the section to the south is owned by Anthem Oklahoma General Partnership. In a quick search, I couldn’t figure out who Anthem is (though I’m assuming they’re not the Anthem of Blue Cross), but that land could be set aside as greenbelt.
The Assessor’s site also shows that most of the land around/under the river is owned by NFL, LLC, which is damn near impossible to find, because they’re drowned out by the NFL in search results…