This is accurate, and depending on the length of the trailer will alter how much gets picked back up by the trailer with weight distribution bars engaged.
Tandem axle trailers usually have an equalizer so that both axles carry the same amount of weigh at all times. Some - do not, usually ones with torsion axles. Without an equalizer the trailer must be dead level (regardless of weight distribution) for the axles to be evenly loaded. In addition, traversing steep roadway transitions, can temporarily unload one of those axles (where either the lead or tail axle's tires are off the ground) to the point where the remaining axle, including tires, springs, etc. is overloaded.
Engaging weight distribution systems 'distributes' the tongue weight (I think of it as the amount the trailer jack lifts when hitching up) across "three" axles:
1. Tow vehicle front axle
2. Tow vehicle rear axle
3. Trailer axle(s)
Since some of the tongue weight gets put back on the trailer when engaging weight distribution, the final weight put on both axles of the tow vehicle is less (fractionally) than without weight distribution.