Not always. But in some cases you are very correct. It becomes a question of saving face and showing power and might. Such a shame really, when emotions are checked at the door and only adults with no private agenda at stake can reach a decision on things like this.
Wife, right now through to the last step, it is union and company, each with equal number of members that will make the decision. Only at the very end will it come to arbitration. Like Running said, it sounds like the first hearing, with the panel getting it next week. Maybe one of the company members will vote with the union, maybe not.
Two things though. First, this is why no matter how easy the case sounds, even cut and dry, you never know how they will turn out. Ever. That is why in some cases, if the company offers a way out, its usually a good idea to seriously consider taking the way out.
Secondly, if the case were as cut and dry as it were presented, I doubt seriously if the company would waste the time and effort, not to mention money to take this very far. I find when I hear a story like this, there are other mitigating things that enter into the over all picture of the employee and the reason they are discharged.