If they did then it backfired.
The other narrative, aside from the Patriots, is that Goodell screwed up Spygate big time. He rushed a decision that left 31 other owners wondering what the hell just happened and opened the league up to questions from congress. He destroyed evidence which spawned dozens of conspiracy theories, and people imagining things that were probably much worse than what was actually on the tapes. Plus, he did all this because he's friends with Robert Kraft, so the theory has gone for seven years.
Then, after getting his ass handed to him in court over all his most recent decisions, he decides to grossly over punish the Patriots, not because they committed a serious infraction, but because it seemed like an opportunity to correct a perceived wrong from seven years prior. Then that decision got handed back to him as well.
I don't think the NFL and Roger Goodell come off well at all. If they were behind it, it surely was cutting your nose off to spite your face.