At first glance, this looks like a technical issue. The person managing the Chrysler account probably meant to send the tweet from their personal account. This is an assumption—I have no knowledge if that's the case or not. But, the individual responsible worked for a firm which serviced Chrysler and was terminated as a result of the communication, so that lends credibility to the theory.
So let's say the tweet was meant to be sent from a personal account. The firm's client—Chrysler is based in Detroit and it's probably not good etiquette to be insulting your client's city given the partnership. So the issue may not be as technical as we think.
The example underscores a fundamental truth in doing business in a connected age. Your employees and partners must understand how to appropriately engage in public (social) spaces. Mistakes will continue to happen because you can't have real time communications in social spaces without human beings doing them. But it underscores the importance in all public communications whether they be personal or corporate. This in particular isn't a technical issue. It's a people (and process) issue.