I think what you're not understanding is that with a weight distributing hitch, the trailer tongue is not just resting on the hitch ball like it is without one.
The spring bars of the WDH swivel left and right to allow turns but they don't freely swivel up and down. There is tension on them. They're trying to force the whole truck/trailer set into an arc as viewed from the side.
When you crest the top of a hill the WDH will not exert much pressure (or any if the angle is steep enough). When you approach a steep upward ramp, the hitch will be resisting the flex that puts on it.
They do transfer weight, mechanically. As others have shown, you can measure it on a scale.