Airbnb makes it easier for naive or unsophisticated "landlords" to rent out their properties. Yes, those would-be landlords should educate themselves about what they are getting into. But you could argue that Airbnb, by dint of its existence and its success, is lowering the barriers to entry for the would-be landlords of the world -- and thus bears a social and ethical, if not necessarily a legal, responsibility to educate or protect those people from common mistakes. And besides, it's just good business to watch out for your customers.
The woman in question was not aware of the problems involved in 30+-day leases. We can fall back on the idea that she was ignorant, and that she got what was coming to her. True. But that's victim-blaming, and it's only half satisfactory. She is the kind of person who would not have invested in, and rented out, a property without the existence of a hand-holding site like Airbnb. Accordingly, Airbnb should do its part to ensure that people like her -- people entering the market because of Airbnb, and who are presumably unsophisticated -- are reasonably protected from rookie mistakes.
I don't think Airbnb is to blame here. I don't think Airbnb owes her any money. But I do think it should be thinking very carefully about how to retool its process, so that situations like these don't pop up again. Not for legal reasons, but for UX reasons. Airbnb operates a two-sided marketplace, and maintaining that two-sided marketplace means balancing the needs of both sides of the market.
It seems that Airbnb is offering to assist her with her legal expenses, and I applaud them for that. No, they probably don't have to do that. But "We don't have to" is a pretty lousy excuse to fall back on. Customer service matters, even if it means protecting your customers from their own mistakes (within reason).