I don't know how much pull he had, but IMO he had a way of smoothing things over when LE ruffled feathers with BVDV and Geoffrey. Once that buffer was gone, it was only a matter of time. LE gave them the perfect excuse.
Definitely truth to this as Pete Taylor was very often the glue that held things together. They eventually made him an associate athletics director. And LE wasn't the only coach to benefit from Pete in this regard. He was a fixer of sorts and a relationship builder and maintainer.
Pete was a fan who happened to call the games. TV wasn't carrying every game in those days, you almost had to go watch live or tune in on the radio. You could immediately tell how the Cyclones were doing as soon as you heard Pete's voice. He was the friend you'd love to sit and watch a game with, as he had the same level of investment as you. John Walters is great, but even he would tell you he is no Pete Taylor.