No reading required (or legal reasoning ability, either)
Actually, peekay.....where to begin?
First, as any rank-and-stoked first year civil procedure student would gladly remind you, federal district courts apply state law all the time - it's called a diversity jurisdiction suit. And your inaccurate statement, by itself, might not bear calling out, but in this instance, you earned it: the Allegiant case was filed in Nevada state court - and if diversity jurisdiction applies, and the defendant "removes" (in effect, transfers even over the plaintiff's objections) the case to federal court, inasmuch as the claims stated in the complaint all are state law claims....you can draw the conclusion. I hope.
Second, I don't have to read the ABX opinion to be able to tell the difference between using public policy, in the form of FAA safety rules, as an exception to the at-will doctrine on the one hand, and on the other hand, basing a claim under the FARs themselves. That is what the court means about rejecting a private right of action under the FARs. The claim for wrongful termination is a state law claim for wrongful termination; and my view (unrebutted by your condescension) is that a public policy exception might well exist under Nevada law - as I said, I don't know - but if it does exist, it would not require, and in fact would have nothing to do with, the existence or non-existence of a private right of action under the FARs.
I guess PPRuNe convention holds it acceptable to fight fire with fire (pun here only unconsciously unintended): so, I hope you fly (or whatever you do professionally) better than you can discuss legal issues in front of a professional, but non-legal internet forum audience.