Carr is saying that they could be awesome people but that they clearly lost their way here. Unless you think the woman is a complete liar...which I for one - with incomplete information, do not.
My point is that he does not have complete information about the situation. Neither do I. Neither do you.
I don't really get why airbnb is on trial here. Something very unfortunate happened. They might've made a PR blunder. Maybe they could have a system with more emphasis on security, probably at the expense of volume. Whatever... it is their company, it makes us hosts good money and us travelers have better experiences. Nobody is obligated to use airbnb. We the users are not the victims of startup founders, like Carr dramatizes in the post, we're just users. We use the services because we derive more value from them than they cost. There is no "social contract" between founders and users.
Airbnb is on trial, I think, because people think they acted like jerks in trying to get someone to be quiet. Internet folk generally do not like people who try to silence others.
Regarding their actual obligations - as far as I'm concerned and legally, the risk is on the host. Of course, for their own benefit it'd probably be a good idea to help her out.