The PGA Tour has a handbook which identifies the requirements to qualify to play on tour and the steps that a player must take to remain in good standing on tour. Among the things a player can't do is play in another professional golf event at the same time as a PGA tour event without the consent of the PGA Board. Clearly, DJ, Gooch, Sergio and the others, except for Na who resigned, broke the rule as PGA Tour players after the PGA Board denied their request for an exemption, and went ahead and played for the Saudis anyway.
The language in the handbook about the grounds to terminate or suspend a player is:
"If in the judgment of PGA TOUR Board he commits a serious breach of these Regulations, the Rules of Golf, the PGA Code of Ethics, or conducts himself in a manner unbecoming a professional golfer."
The issue comes down to whether the PGA Tour correctly applied the rule (which they did as playing in a competing event without a waiver violates the PGA Player regs), and whether the rule prohibiting players from competing in rival tours is enforceable. Don't think the answer is a slam dunk for either side, but it would seem that the PGA has the better argument as the PGA Tour has a reasonable interest in protecting the quality of its fields, and as stated above, there are other tours, including LIV, where golfers can seek to earn a living. Further, there are opportunities, which every PGA player has taken advantage of, to play and earn money in non-PGA sponsored golf events. So, it's not like as soon as a player earns his Tour Card his only avenue to make a living is via PGA Tour. He can earn money outside a tour, but not just events that are played during the same time as a PGA event without permission. The players that went rogue can claim that the Tour is haphazardly and unfairly granting exemptions as it has previously allowed players to play in other events (e.g., Harold Varner III beat Bubba Watson is an international golf event earlier this past Winter on the same weekend as a PGA event).
It seems to me that the financial strength of the Saudi Tour is actually an argument that hurts the players' argument that they should be able to play in whatever events they want as it's pretty hard to for DJ to claim he's hurt by the PGA Tour's rule as he took $125 million to play on a rival tour. I'm sure every player that jumped to the Saudi Tour took more money from the Saudis than they ever made on the PGA Tour; so, what's their damages? They are all in a better financial position then those rubes that stayed on the PGA Tour.
So what if DJ and Sergio can't play in the John Deere Classic ever again? Is that going to be the damage claim?
If those players try to make the argument that the PGA rule may keep them from playing in the Masters and US Open, then, because the PGA doesn't control either of those organizations, the players will need to sue those organizations as well.
Seems like the players that want to play on the LIV Tour should resign like Na did. If that LIV folds, they can apply for re-instatement and after a brief suspension it would be granted. Looking for the Courts to resolve this will only result in lawyers getting richer...
