I can't imagine a court upholding a lawsuit by a dealer, for a few thousand dollars for a new vehicle. Now if the paperwork said $3,000 instead of $30,000 for a brand new truck or car, then reasonable minds would say it was a typo, not the negotiated deal, and the deal couldn't stand as is. But if the dealer said that the sales guy sold that same vehicle for $1,000 to $3,000 less than he should have (after being reviewed or not by a manager), then most any judge would toss out that lawsuit. Assuming it would get that far which wouldn't really make any sense. Sounds like there are quite a few dishonest dealers out there.
In the reply to the OP I'd probably say to the dealer that it sounds like an honest mistake, but why are you asking me to solve it? After hearing the lame excuse, I'd ask what could you do for me, given that this really is not my problem. Getting 6 free oil changes and tire rotations, or maybe some all-weather mats might be in play. I wouldn't ask for a cut of the incentive.