The article that you refer to does not say that the network picks the halftime acts. Moreover, due to the Janet Jackson "nipplegate" controversy, the NFL dropped their production contract with MTV. A more recent article even refers to the NFL as asking artists under consideration to play the halftime show to agree to pay the NFL a share of their later earnings.
NFL Asks Musicians for Money to Play Super Bowl. I do not mean to be obtuse or fractious, but surely there is some website or authority that clearly and directly addresses and settles the issue.