I sort of understand where you are coming from. This is from Eaton's website about the truetrac:
"When a wheel encounters a loss of traction or the terrain changes, the gear separation forces take effect and transfer torque to the high-traction wheel. The helical-shaped gears mesh with increasing force until wheel spin is slowed or completely stopped. When the vehicle exits the low traction situation, the differential resumes normal operation."
So one wheel has to be spinning faster than the other for the biasing to the other wheel to take place. This is where I would think that traction control would hinder its operation.
On the other side, there has to be a certain amount of torque being applied to the diff to get the operation started. There is very little torque being applied when a wheel is off the ground. Therefore the truetrac can't do its stuff. By applying the brakes slightly (or traction control) it gets the process going.
So it needs a certain amount of resistance on the spinning wheel to work, but it still needs the wheel to spin to transfer (up to 70%) torque to the other wheel. So by applying the brake briefly will work alright. Still not convinced that traction control would allow enough wheel spin to get it to work fully though. But I have been wrong before.
I am also not sure that I would think to apply the brake when I am trying to drive up a hill. You would not know that it was in the air in order to apply the brakes until you came to a stop anyway.
All interesting stuff and I now know that ATB stands for Automatic Torque Biasing diff

