I had this exact discussion with my in-laws.To OU it is just Bedlam. Texas is our main rival and OSU is not nor has it ever been. They wish they were.
I had a good buddy who is a very accomplished architect in Dallas. He helped me coach a couple of teams. He is an OSU alum. In that time frame, OSU beat us a couple of times, and he and I had the discussion about whether or not they are OUr rival. They beat us in 01 in Norman, then again in 02 in Stillwater.
In 03, Lester was their head coach. It was the year when he gave his "let er rip" pre-game interview with the sideline reporter, I think from ABC. We beat them 52-9, much to his disappointment. I told him that's what you get, when you make us give you OUr full focus, rather than just another game, which as you said, they usually were, and mostly still are.
Since the back to back 17 years ago, they have won Bedlam twice. Bob's re-kick was one. And in 2011 when they went 12-1 and won the conference, we played them up there and were missing a dozen players in the rotation, and they kicked us. So since 2002, we are now 15-2. As I told my buddy in 2003, that's what you get if you're an OSU fan and you have OUr full attention.
I like the Bedlam label, primarily because the national talking heads like referencing it, and it makes is seem nationally relevant. Can't hurt when lobbying for a top four ranking, especially when they were ranked 21.
Since LR seems to want to call it a rivalry, I won't dispute the claim. My soph year is still me favorite Bedlam game. We won 66-6 eighth ever wishbone game for OU. And Jack Mildren and Greg Pruitt gave the fans at Memorial Stadium a hint was what laid ahead in 1971. 66-6 seemed to have so much symmetry.