Sure they do. The union controls the grievance process. If they don't want to file a grievance, and they have a legitimate reason, they don't have to. Most unions just file any disciplinary grievance to avoid DFR litigation, but they certainly have no requirement to file the grievance if they feel it is without merit.
Absolutely not true.
The union MUST file a grievance if requested by the grievant PERIOD. The grievant is the one that is entitled to all of the contract protections and to have their case heard all the way through and including the full System Board if that is what is desired.
This is not just a discipline hearing matter either...this would apply to any grievance technically, however, everybody is more careful in a termination case obviously because of the HUGE potential liability.
For non-termination cases, if the grievant is wrong, it is very difficult to win a case when the Grievance Chairman AND the company lawyer both testify in front of the arbitrator that the pilot is wrong about what the contract requires...but it is still the grievant's right to do so.
As far as not initiating a go-around below 400', SWA would have to show that they terminate everybody that doesn't initiate a go-around below 400'. Also note that it is required to deploy the spoilers after landing, was that Captain fired? This isn't as much of a slam-dunk as you are making it out to be.
As far as totaling the airplane because of a mistake, SWA will run into difficulty if they have not terminated everybody that wrecks an airplane.
I have a feeling they offered her some hush money to resign and she refused...hence the firing.
Also realize that in the termination hearing all the CVR/FDR information, and hence, most of the NTSB stuff findings will be out since they will be based on the contents of the FDR/CVR's. So all you have is what the FO said happened...what the Captain said happened...what is on the tower tapes...and the fact that you have a 737 with a busted nose-wheel.
My prediction is once the real lawyers get a hold of this she will "retire" with a nice little nest egg, with a signed non-disclosure agreement.