Not quite. First of all, an important distinction: AIG is suing no one yet. The former CEO of AIG, Maurice Greenberg, is suing independently on behalf of shareholders. This backs AIG into a delicate position:

If the [AIG] board does not give careful consideration to [suing alongside him], Mr. Greenberg could challenge its decision to abstain.

Should Mr. Greenberg snare a major settlement without A.I.G., the company could face additional lawsuits from other shareholders. Suing the government would not only placate the 87-year-old former chief, but would put A.I.G. in line for a potential payout.

Unfortunately for AIG, this would probably be seen as the worst PR move by a corporation since Exxon-Valdez.

Now they're suing the federal government for not paying their shareholders?

Sort of. Specifically, shareholders are not held liable for the actions of a company, and what the government did to AIG is a bit like eminent domain ... they just took over majority (google terms of AIG bailout for some info). They're going to argue private property seizure, and probably misuse of stockholder's investments ... and I'm not sure how that will work, because there ought to be a precedent somewhere -- there've been bailouts before, after all. I'm assuming they'll get more or less laughed out of town, but you can't underestimate money.