Steering wheel angle while towing

Given the rarity of this issue, blaming P-metric tires makes ZERO sense. The vast majority of light truck users, and just about everyone down from there, uses passenger tires. Not to mention, no F150's are known to do this, unless there are suspension wear, trailer, or trailer hitch issues. Bottom line, not likely the tires. Could be something amiss in the EPS system, but this all seems odd, because anyone who owns one of these trucks knows they don't tolerate sway, and they don't even tolerate a steering angle that doesn't correlate with the direction of vehicle travel / polar moment.