Yup...when it comes to schedules, the Networks are the ones who have the power and control here. They pay good money for that right.
I am sorry but this is unequivocally false. I have a good friend who was one of four individuals responsible for creating the NFL schedule from about 2011 to 2017. They once gave a presentation to all the coaches describing how the schedule is generated and Pete came up to my buddy afterward and told him never to give that presentation again and that knowing what happened behind the closed doors of the scheduling room, which even the commissioner didn't have a key card for, was "terrifying".
But go ahead and fantasize that you actually know the ins and outs about how this is done. Networks have some limited control, but the NFL itself is king of the schedule.