The '03-'04 6.0L's got the short end of the towing capacities. CGWR was capped at 20K, after 2005 got the upgraded springs and brakes the DRW's went to 23.5K (26K with the TowBoss)
From the rating's perspective, you're limited to 12.4K, and that's something your insurance company and the laws in your state may hold you to if something happens. For the most part (and this is an at your own risk short of thing), as long as you keep within the GAWR's and GVWR's the DOT won't give ya too hard a time about it, unless you sag so much its noticable.