I think the state legislature will make sure that OU and OSU are in the same conference, just like the state of Texas will put A&M and Texas in the same conference.
Where does the Oklahoma legislature get that authority from? Threaten to cut off funding maybe? Well, I don't think that is going to happen. Change the law to take power away from the Regents? That takes time, and would be heavily blocked by those advocating separation of powers. Here is the role of the Board of Regents:
To maintain academic independence from state politics, the Oklahoma State System of Higher Education was created in 1941 through constitutional amendment (Article XIII-A), governed by the Oklahoma State Regents for Higher Education. The State Regents prescribe academic standards of all higher education in the state (for both public and private instututions). The State Regents also determine functions and courses of study at public colleges and universities, grant degrees, and recommend proposed fees within limits set by the Legislature. In general, the State Regents receive a single higher education appropriation from the legislature and have the constitutional responsibility to allocate those budget items to each Governing Board of Regents or Board of Trustees of a constituent agency.
Based partially on the above, and the intent of separation of powers to protect the state's universities from too much legislative interference, I'm guessing that without a constitutional amendment (which I believe would have to be voted on by the people), the Board of Regents for the University of Oklahoma would make the final decision for OU, and same would go for oSu as to what conference they might join. In any event, I don't think that this is an issue that an elected official would want to touch with a ten foot pole as they can claim they don't have the authority (and thus the responsibility) for anything that may happen.
I think it is better than 50/50 that oSu would be extended an invitation to join whatever conference OU was invited to, but that isn't a guarantee. Not sure where this aTm is handcuffed to UT thing by their state legislature comes from either. Certainly wasn't an issue with the formation of the Big 12, so it sounds more like conjecture more than anything. Ann Richards "pushed" Baylor on the B12, but in reality, the B12 wanted one more school, Baylor just had the most support. Truth is, nobody knows what will happen, let's just hope that oSu is extended an invite and it is all moot.