When I read this my first reaction was that 13% and 15% both sounded high. I've always used approx. 10%. Since I wasn't sure which was more common, I did some searching and found an interesting article about the SAE, the OEMs, and the hitch manufacturers working together to create newer, updated standards.
The committee settled on 10% tongue weight for conventional trailers and 15-25% for 5th wheel trailers.
I don't think SAE is saying that travel trailers should have 10% tongue weight. I think they just decided that 10% would be a representative value for a wide range of "conventionally hitched" trailers.
In this forum, we tend to forget that travel trailers are just a small part of the population of trailers which are towed by conventional hitches. Optimum tongue weights for some types of trailers might be around 5%. Others might need 15%. The "standard" value of 10% seems to be a good compromise.
Your OEM receiver has two ratings, often called a class 3/4, without weight distribution and with. Over 500 (maybe 600) pound of tongue weight requires weight distribution for your truck. Use one with integrated sway control and you'll be pleased with how your truck performs.
A & A parents of DD 2005, DS1 2007, DS2 2009 2011 Suburban 2500 6.0L 3.73 pulling 2011 Heartland North Trail 28BRS 2012 VW Passat TDI