Well, what I've seen of Heidenreich I've liked and I find her suggestion intriguing, but I think it might be REALLY hard to accomplish unless you are a very talented trainer. I could see it working for screaming, but biting seems really challenging in that respect, for example. It would also rely on rewarding the cued behavior frequently while not rewarding the behavior when not cued. It does put a different spin on things. But I don't think it would be the first thing I'd try.
In "Good Bird" in the chapter on Biting she uniformly says "Don't try to force your bird to do anything it doesn't want to do" and "Use positive reinforcement to make your bird WANT to ____ (step up, come down, be with an unfavored pesron)", But for the situation where the bird gets too rough while grooming or playing with you, she does say, "End the interaction, give your bird a "time out"'. I don't have the impression from this that she's a whack job, or that she doesn't use multiple forms of behavior modification. However, like many people when addressing a lay population, she tends to use the word "punishment" in the vernacular, not in the technically correct sense. I think there are other cases in that book where she uses punishment without calling it that.
I do agree that it is difficult, and in some cases not desirable to not react at all to biting. If Scooter is nipping at me because he wants me to pay attention to him and not the computer, I can ignore that just fine. But when he was all revved up and angry, I needed to do something to get my flesh out of reach of his beak even if that meant reinforcing the behavior. And all he could really do is nibble me to death, or scar my hands... a BIG bird could be doing real damage to body parts, as in permanent defacing or crippling damage, and I think it may bear stating the obvious that if your bird is really injuring you, you should find a way to make it STOP even if it does net damage to your training attempts or your relationship. If it doesn't actually injure the bird seriously, it's fair game if your ear is being torn off... But once you've extracted yourself from danger and are back in a training model you should try to avoid putting yourself back in that situation while attempting the training. Does that make sense?