The dynamics of the conference were different before Nebraska and Colorado left. There was much more of a North v South among the schools. Texas and OU, together, mainly controlled the Big 12, which is the main reason Nebraska ultimately left. Missouri also carried some influence due to the Kansas City market. It was in that environment the idea for a network was pitched. Nobody thought a third tier rights network would get off the ground, the same reason A&M initially said no.
Texas does control the Big 12 now because without Nebraska and Missouri, Texas is the only school capable of keeping the conference afloat financially. So yes, Texas does control the conference now, though it still likes to do everything in step with OU. But the current conference makeup isn't what existed while a network was being discussed.
Once the LHN was born, everybody wanted a piece and Texas told everybody to fuck off after doing all the work themselves. That, the instability due to TV contracts ending and Texas not committing to the conference, and A&M's little brother syndrome were the catalyst for Missouri and A&M leaving. Nebraska would have left even if the LHN was never created.
For the record, I wish the Big 12 would die. The quality of football is actually really good but the perception sucks and the conference footprint is way too small. Ideally, the ACC and Big 12 would take their best schools and combine. Something like Texas, OU, TTech, OSU, WVU, Clemson, FSU, GTech, UNC, Miami, Louisville, Duke, Kansas, KState. That would be stacked football and basketball conference with a massive footprint. Won't happen, oh well.