After reading this yesterday, i was crutching in to the house and looked at my wrecker. There doesnt seem to be a lot of room on the rear axle to bed for 16s. I had 14s on it previously and both rear tires had some chunks taken out and a radial gash in the treads. I now understand what could have caused the damage to the tires.
Here is an 816 with 16s. Not my rig, i borrowed it.
View attachment 850945
Not a lot of room on that right rear tire and wrecker bed. There is a cubby/storage box on both sides, that could probably come out and modify the mud flap support and gain a little more clearance.