The thing he ignores here is the value of your own time. Call 8-10 dealerships? Two FULL weekends? On a run of the mill kind of car (like a Honda, Toyota, etc) the most you can possibly save this way is probably $500-$1000 (getting bank financing and selling your old car yourself are more, and probably worth the time it takes).
I don't think it's worth my only non-working time to save that kind of money. Now if I were buying a BMW or other high-margin car, maybe....