The leverage is the TV contract money. If SEC isn't able to schedule big name out of conference opponents (from the Big Ten, ACC, and Pac 12) that brings down the value of the SEC TV deal in negotiating.
I'm sure there will be exceptions for existing rivalries (Florida v FSU and Clemson v S. Car), but its a good strategic move to combat the increased value the SEC will now have with addition of Texas and OU in the SEC TV package.