This is NOT sway you are talking about here...
Sway is an uncontrolled oscillation of the trailer that gets worse unless corrective action is taken. If it stops by itself, it is definitely not sway. Sway is an inherently unstable condition. When the trailer corrects itself, it is demonstrating that it is inherently STABLE.
You are referring to "push-pull," or "bow wave effect" here.
Of course, the mitigation is better sway control, which then makes me look like I'm contradicting myself... The thing is, what you're trying to achieve is a more rigid connection between truck and trailer, at least in the yaw axis, so the whole thing moves as one. That's precisely what sway control does, to control sway. This is a happy side-effect.
You don't get nearly as pronounced of an effect from a 5th wheel or a Hensley/Propride hitch. This is because the pivot point is at, or is projected to, the center of the rear axle where the slight side force has no leverage on the truck. A conventional bumper hitch has 3-5' of leverage on the rear axle, making the effect much more noticeable.