HUH. as soon as you said that the woman had a child diagnosed with Autism, the very 1st thing that popped into my head was, "Where is he on the spectrum?" Although this woman may well have been in that parental shock/grief looking for empathy phase, it doesn't mean that it is okay for her to expect every single human being that she knows (she did post this info to her Facebook page, right?) to detect that from a written text (written messages are devoid of expression, tone & inflection making misunderstandings even more likely) & respond accordingly.
Does this woman know that you're an Aspie? If she did it might make her understand why you'd ask such a question. Many of us with Asperger's don't view ourselves as such sad, pathetic, tragic creatures. Such a diagnosis isn't the end of the world: obviously she had observed something atypical about her child & didn't know what it was, how to handle it or what the implications might be for his future. Once you have a definitive diagnosis, a context is immediately provided for the behaviours her child exhibits. In other words, knowing what the 'problem' is is half the solution.
As a parent myself I GET that no parent wants to hear that something about their child is 'different' (read WRONG read DEFECTIVE). Sometimes, I've seen this personally, the parent goes into histrionics upon receiving a diagnosis for their child seeking sympathy & support from anyone who'll listen. It can almost look like Munchausen's By Proxy (except that they haven't induced the sickness in their child to gain sympathy) This histrionic Munchausen parent then often becomes one of those so-called tireless crusader types loudly trumpeting their cause celebre. the CHILD who has to LIVE with both the symptoms of his condition AND the consequences of being officially labelled can get kind of lost beneath the parade float.
This can happen because some NT types are emotionally overwrought. YES, I know we Aspies are all emotionally challenged BUT many NTs are emotionally challenged too: only in the other direction! Finding out that your child has some awful form of terminal cancer is a truly tragic diagnosis & if a person of any sort goes off the rails upon hearing such a thing, weeeelll.....they get a free pass. Discovering that your child is an Aspie isn't a disaster. Perhaps her limited knowledge about AS is the cause of her alarm: maybe she thinks he'll never be able to live a satisfying life? Then, too, perhaps she was observing some extremely severe Autism spectrum symptoms (of the hockey-helmet head-banging completely non communicative type...) BUT were that the case, she wouldn't have needed anyone to tell her something was indeed very wrong.
Please don't beat yourself up over this woman's having taken undue offence. Every emotional reaction of an NT doesn't make the Aspie automatically wrong by default! YOU intended no offence whatsoever. You weren't rude, insulting or mocking. She'll probably cool her jets after her grieving process abates & she begins accepting the diagnosis & realize that you really didn't say anything truly insensitive or mean-spirited.