Good question, so I looked it up in our contract.
I will quote Article 22, paragraph G.
"The Company, the Union, and the pilots will use their best discretion when communicating information regarding the parties. Communication shall remain respectful at all times and at no time shall any party slander, defame or libel another. This includes all venues including but not limited to: the Internet, written or verbal."
So...
Since the union agreed to this contract, I imagine they wouldn't have much to say if SW's identity were to be unearthed and he/she WERE terminated on the basis of what they'd posted. I think it's fair to say that StopWex's communications thus far have been anything but respectable, and certainly meet the definition of defamation, if not necessarily slander or libel.
I believe that the company would only have to write a threatening letter to the FlightInfo board moderators and they would basically HAVE to hand over the e-mail address of Stop Wexford, if prior knowledge of these "public" forums is correct, one would think that they would already know who it is if they really wanted to know... Or by other methods, for that matter, if they were sufficiently interested. See the "Skywest Hiring" thread for another example of this.
StopWex would like you to believe that the company has actually found out who they are and has threatened them with termination, but I find that highly unlikely... Sounds like more chest-thumping, along the lines of earlier self-puffery that suggested that people were having "intelligent" discourse about company matters in the PIT crew room merely because of the inflammatory posts they'd posted earlier. Oh, please.
(edited for grammatical error!)