I think the whole idea of just PTS is a really arrogant human approach.
Not that I expect the OP to be able to answer these things, but is the dog a rescue (maybe has underlying issues)? How old is it? Is it new the household? Is it used to having house guests? Had it been behaving unusually during your stay? Was it sitting/resting in its safe place (suggesting it may have needed be alone, or feeling anxious). Was an escape route suddenly blocked, and the dog felt cornered? And what exactly happened, was your DD staring at the dog, things like that.
The owners definitely need to take it seriously and make a big effort to deal with it, but unless someone can without doubt say there was absolutely nothing wrong at the time, its not fair to condemn a dog to death for it.
My 2 dogs are not used to house guests, so are never left alone with any guest, if we get up to make tea for example we call the dogs to come with, if they start behaving anxious they get put in their bedroom (utility room) and everyone is told to leave them alone, and someone will spend time with the dogs to calm them. If people behave in a way that will provoke a dog we tell them to stop, i.e staring, growling. We introduce new children very carefully, I never assume that any child knows how to behave around a dog even if they have their own, I supervise everything.
One of my dogs did bite someone once, a guest who knew we had small dogs, 'forgot' stumbled into him, kinda booted him in the ribs in the process, and then stood on his foot with their shoes on, and broke his toes, he bit her in the ankle, I in no way see any issue with that, as from what I saw the bite was because she was still on his foot.