This would be a good job for him to take. A relatively low-pressure gig at a school he's familiar with. He's not likely to land a "destination" job next time around after his experience at Michigan. Wherever he goes next will probably (if all goes well) be a steppingstone to another high-level job. So he may as well take this if he can. He probably has a greater chance of success at Tulane than at Ole Miss.
Remember when we were arguing with Rutgers bloggers about which athletic director was worse?