No, we don't know what the contract says. There could very well be an escape clause whach states something to the effect of "(Insert name of production company here) reserves the right to cancel for the following reasons: yadda yadda". I doubt that the family filed the suit on their own--they most likely hired an atty to file for them. If the atty was any good at all, he'd have read the contract before filing and decided what the merits of a possible case would be. The emotional distress, IMO, is just in there as a scare tactic. Intent to cause distress cannot be proven here. Breach is a more definitive argument.
Aha. There is the problem.
I would be willing to bet that there is no merit to this case, because ABC, I'm sure, is completely protected in the contract against these sorts of claims.
However, there is no shortage of attorneys who will file suit against big corporate, even without merit, in the hopes they can get them to settle.
Sadly, I think you are right about this case being settled. That is one of the many reasons our country is so sue happy. Atty's know that the vast majority of companies will settle any case, simply to avoid the expense of fighting it, as well as to avoid any kind of P.R. nightmare.
Getting something for nothing, and sticking it to big corporate. It's the American way.