Couple reasons:
1. They can't sign him otherwise. Example - Clips will only have a room exception this summer. Lets say they use that to re-sign Collison or sign a big. Well, then they cant do anything else. But lets say they like Aminu. They can have the Pelicans do a sign and trade where they send us Dudley. This could apply for several teams, most notably ones that have trade exceptions left over from previous deals but no cap money.
2. Since we have Bird Rights, we can give him a contract that allows us to increase or decrease his salary by up to 7.5% each year, as opposed to 4.5%.
#1 is the most likely outcome. There are 18 teams currently that have trade exceptions that allow them to just accept a player onto their books without having to give anything back. Some of those teams, like Brooklyn and the Clippers, dont have much flexibility so something like this woul be one of the only ways to acquire a guy in FA outside of the room exception and veteran minimum deals.