A few things, you're right that Barca is not La Liga. As I know there's no proof that Barca pressured La Liga to act. You can understand why people might suspect that, though it's all conspiracy theory passed off as fact on here.
However, Barca'a FFP complaint is most certainly not normal. It's the first time I remember any club complaining to UEFA about FFP over a transfer.
Finally, Barca is apparently suing over breach of contract. It's not unfair to consider that moaning. It's also a it rich since both Dembele and Coutinho have apparently gone on strike to force transfers. It's the modus operandi of unsettling players, and having them force their way out of clubs that leaves a bad taste. Suarez, Ronaldo, etc. it's certainly not Madrid and Barca that employ such tactics, and United are no angels, but it seems to be standard operating procedure for Barca. That's why people revel in the karma. Also, United and Pool didn't sue over Ronaldo or Suarez, doesn't look like Dortmund will over Dembele either. That's why it looks like sour grapes.
However, I think people should be careful before they revel too much. City and PSG are practically owned by nation states, Liepzeig seem to benefitting from support of a major multinational company. We'll see what Bayern fans will have to say if Liepzeig start winning the Bundesliga. Imagine if the Saudi Royal family bought Espanyol and start spending billions. That's the reality United fans have had to live with since the noisy neighbours got bought by Abu Dhabi. That's why you'll not find much sympathy here.