A WDH will put some tongue weight on the trailer axles, which seems near 20% for those who have measured their TT weights. So what you call true tongue weight is tongue weight and what you measure is only the amount of TW carried by the truck's axles.
Here's an example:
TW measure by something like a Sherline scale: 1000 pounds
Drop the tongue on the ball:
Front axle decreases by 400 pounds, rear axle increases by 1400 pounds. This is the net 1000 pounds of TW.
Now apply WD to restore 100% of front axle weight:
Front axle same as unhitched, rear axle is now only 800 pounds, and trailer axles went up by 200 pounds.
So the efffect of TW on the truck's axles is 800 pounds which goes towards payload/GVWR. The effect on the receiver is 1000 pounds which should be checked vs. its limit.