What, exactly, is exteranal air anyway? I am surprised this post went for 4 pages and none of you flamers caught this.
Um, duh, air conditioning! APU is good for providing electrical power and the 'alternate' source of 10th stage bleed air via the APU itself by opening up the load control valve and isolation valve.
Essentially, what they are saying is that if you have external AC power, and external air hooked up to the airplane, you don't need the APU on.
But kudos to those crews who run it anyway. Let our management deal with fines "in the millions." Give us a new contract, and I guarantee all pilots will go out of their way to help the company. As of right now, morale is low.