The main reason is to allow the differential to break in before putting it under load. The gears as assembled need some heat cycles to break in and seat. Prior to break in there is a higher degree of deflection that could cause issues under heavy loads. Dodge and Nissan both had problems with rear diffs spitting teeth due to heavy loads being placed on the diff before it was broken a few years back. You can probably Google Nissan Titan and busted diff to see some of the carnage. That being said I have yet to spit a diff on a Chevy or a Ford due to tow loads. I don't like to exceed 3/4 of the rated tow capacity so I probably never pushed my luck. You may be fine and likely will be fine. In the old days rings required 3000 miles to seat but now a days with the tight tolerances, synthetic fluids and materials used I don't know if that is still an issue. The 1000 mile recommendation is a cya from the factory. My class C rolled out of the factory fully loaded and didn't have any problems and I tow 3500 lbs behind it regularly on top of the vehicle being near GCWR.
If you spit your diff at 15000 the dealer will likely ask you if you broke in your truck prior to towing.