That guess about Gibbs sounds logical to me.
A lot of people have been fired for accidentally tweeting on their business account when they thought they were tweeting on their private account or they send a private e-mail to "all" or "everyone".
I suspect this is what happened to Gibbs. Now they are trying to claim they were "hacked". If they were "hacked" then the hacker didn't really take advantage of it, did they?
Usually when an account is "hacked" there is a whole bunch of stuff that is tweeted or posted.
Nobody hacked McDonald's twitter account.
Occam's Razor tells me that the person they should be looking at is the guy who has to approve every single tweet from the company. As vice president of communications, that person would necessarily have to be Robert Gibbs.