More likely OU would build the medical center (or better yet takeover Hillcrest on 11th) and expand its OU Health offerings in Tulsa. TU with its joint venture partnership with OU would also have a place there. Similar to how the different schools share facilities at Texas Medical Center in Houston.
I don't think Texas Medical Center is ran by a specific university though is it? I think it's a non-profit entity that just oversees the area and each school has it's own complex within the Texas Medical Center and are stand alone schools/programs. There's no Baylor-University of Texas school of medicine or A&M-Baylor, it's just Baylor, A&M, UT, etc. schools that just all happen to be in the Texas Medical Center. It's not odd to have medical schools clustered together but not sure if I've ever seen a partnership like OU-TU. Where one specific university seems to be the dominate school (for medicine that would be OU). Do people that graduate from the OU-TU school get degrees from both schools? When you pull up the website for the school you go directly to OU.edu, I don't think TU even has a website for the school of community medicine. The only part on TU's website is for Oxley College of Health Sciences (which is part of the OU-TU partnership I think). It would make more sense to me if say OU and TU bought Hillcrest together (as an example) and rebranded it 'Tulsa Medical Center' or something and were partners in ownership then each university had their own degree programs as a University of Tulsa or University of Oklahoma and just had shared access to facilities and offices versus having a co-branded school like now.
I mean if your degree says University of Oklahoma when you graduate the OU-TU school of community medicine, what's the point of having TU as a co-brand partner in name only? That's kind of the main point that is confusing to me about the partnership.