After reading all this and the mathematical attempt from the other thread, I get the feeling that we are missing something.
Assume for a minute that the tow vehicle has no springs. if you attach the trailer to this imaginary vehicle, the hitch ball will drop toward the ground and the Tow vehicle front end will become lighter. The primary fulcrum at this point is under the rear tires on the tow vehicle, the hitch ball provides flexibility but really plays no part in the behavior of the system beyond transferring the tongue weight to the tow vehicle.
Now consider the Weight Distribution Bars (WD) which are attached to the frame of the tow vehicle through the hitch. The bars run parallel to the frame, not necessarily in line with the frame but forced to be parallel by how they attach to the hitch.
Now jack up the tongue so that the trailer and tow vehicle are both level. Attach the WD bars to the frame of the trailer, so that the WD bars run parallel to the frame of the trailer. Assume that the WD bars don't flex and since the imaginary tow vehicle has no springs, it can't sag under the weight of the trailer. There in now a new primary pivot point centered around the hitch ball, the rear tires of the tow vehicle are no longer directly involved. The levers are made up of the vehicle frame which is extended using the WD bars to the other side of the hitch ball and the trailer frame which ends at the hitch ball (fulcrum or pivot point).
When the tongue jack is removed, everything stays level, all the tires of the tow vehicle stay on the ground. At this point the tongue weight is being distributed evenly between the front and rear tires of the tow vehicle.
The forces around the ball and the rest of the hitch are quite complicated and are best left to the mechanical engineers to explain. Adding vehicle weight, springs, and bar flexibility are required for a functional system, but the math gets very ugly and probably doesn't help understand what is happening.