Who says it was breach of contract? We have no idea what the contract stated. For all we know, she simply signed a release form, releasing the show of liability if something went wrong during any surgery.
I highly doubt the show signed something saying, "We'll do this no matter what, and we cannot change our minds."
I am a cynic, and I think this family is just looking for an opportunity to sue. That is where most lawsuits come from.
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.