Thanks for the feedback, everyone. I realize now that I was probably being too harsh. There's a good chance the woman's daughter was allergic to nuts; giving her the benefit of the doubt, I'll say she wasn't a liar, just inconsiderate.
Let this be a public message to anyone with any kind of allergies. Whenever you eat out, please let your server know your dietary restrictions up front; as it's been mentioned, some dishes may contain ingredients you're not aware of, so play it safe. You may think your allergy isn't a big enough deal to mention, but if you have to send your food back because it contains the thing you're allergic to, then it is a big deal. Please just save everyone involved some time and money.
Of course, if you don't mind a little swelling or itchiness, then go nuts
It's your call.