He also has several other things going for him. He has lots of experience fighting the legislative battles and knows how to fram arguments in that context (if not in the context of a presidential campaign). He also has lots of folks on the Hill who still remember him positively from both sides of the aisle. They know how he acts when he's actually able to lay down positions that have the likelyhood of being agreed to and, more importantly, stuck to. Finally he has literally nothing to lose and this offers him a fantastic opportunity to build a lasting legacy, perhaps one more significant than if he had won the Presidency, and certainly a better one than his being the loser to Bill Clinton in 1996.
As you say, he has a stake in the outcome, if not for his own treatment but for the treatment of his brothers (and sisters) in arms.
Shalala, on the other hand, will be at the table representing AFSCME and the bureaucracy. She'll also be all about protecting the Clintonistas from any hint that this might have been a problem prior to 2000 or, perish the thought, could be the result of the slash and burn policies of the Clinton administration in treating the US Defense budget as their private piggy bank.
All true, but she'll also be there to make sure that, one way or another, this commission will be perverted into a weapon to be used against the Republicans in the upcoming elections, like the 9/11 "Commission" was. If she can't steamroll Dole and the Iraq veterans on the panel into making the commission report a political hatchet job against the Bush Administration, she'll walk away from it and claim the panel is trying to "whitewash" Bush and Rumsfeld, thereby discrediting it.