You cannot reward aggressive behavior, this is a myth. Aggression is a distancing signal. The dog is trying to communicate that something in their environment is making them nervous or emotionally aroused.
Aggression isn't simply a chain of behavior, it's behavior that is the direct result of emotional stress. Introducing rewards to a dog who is being aggressive to curb that response works (when delivered properly) because you are trying to change their emotional response to a given scenario by associating the thing they are reactive to with something positive. Saying that giving rewards encourages aggressive behavior is a bit like saying that if you give a child a reward for swimming when they are nervous, you will teach them to be afraid of water. What is actually going to happen is that you will teach the child that water means good things, and before long swimming (a fun activity) will become self-rewarding.
This is called counter-conditioning, and here is a great video showing how it works
https://www.youtube.com/watch?v=sI13v9JgJu0
It sounds like 2 things happened with the trainer you saw.
First, there was an escalation on the ladder of aggression. This may have had nothing specific to do with the person (he may simply just be becoming more reactive to people coming in the house in general), or it may have been because her body language and focus was constantly on the dog, and that made him uncomfortable (presumably when you have people over they spend most of their time ignoring the dog, and that is a lot more comfortable for nervous animals). Either way, he was simply stepping up his reaction because his previous signals (barking) did not make the threat go away. He did the only thing he thought he could do, he tried to signal harder to get her to leave.
Here's a good video on escalation of aggression
https://www.youtube.com/watch?v=HL4_...1&feature=plcp
Second, it sounds like the dog was over-threshold. She moved too far, too fast with him and he was unable to become uncreative because he couldn't give himself adequate distance between himself and the threat. Houses are very closed in spaces, many dogs become reactive when they feel like they can't self regulate and remove themselves from the situation. We're dealing with the sympathetic nervous system here, fight or flight. Most reactive dogs are at their worst in situations like this because by default the flight option has been removed.
Also, I think the reward system she was using was a bit off. Dogs are very specific learners. By calling him to you and rewarding him when he became reactive, you were rewarding his coming to you, but not addressing his emotional response to the trainer. In his mind, he got a treat for obeying your command and coming (something he has probably rehearsed with you many times), not for anything to do with the other person in the room.
I would have either had you work at a distance and rewarded him for calm behavior and looking at the trainer and not reacting, or had the trainer deliver the rewards while maintaining non-threatening body language.
By all means hunt around for a better trainer, but avoid anyone who suggests physically or verbally correcting the dog for this behavior (removing the dog from the situation is a good alternative). This is a fear response. Punishing the dog will only eliminate their attempts to communicate their discomfort, but will not address the underlying emotional state. You will create a dog who may react very aggressively "without warning" because they have learned that their more polite signals will earn them punishment, or, alternatively, you will see an escalation in their behavior because they have learned that people coming to the door = stress = punishment. They will try even harder to keep people away.
Your best bet is slow counter-conditioning to approximations of people coming in the house (i.e. doorbell ring = food, door knock = food - obviously you want to work where you reward him for not reacting to these), giving him a job like 'go to your mat' for when people come in (teach an alternate behavior to reacting) and to have guests be really non-threatening when they come over (the old "no talk, no touch, no eye contact") and drop food for him. I say drop, because you don't want him to feel like he has to engage with them for a reward (right now, you can up the ante later), just to tolerate them in your space.
Oh, and the dominance thing? Totally bunk. Been disproven in scientific circles for more than 40 years. I'd forget it and concentrate on learning his body language and signals so that you are better able to predict when he is about to become reactive and you can head him off.
Here is some resources that may be of some help?
Longblades already covered "control unleashed"
http://www.dogwise.com/itemdetails.cfm?ID=dtb825
http://www.dogwise.com/itemdetails.cfm?ID=DTB527
http://ahimsadogtraining.com/blog/bat/
https://www.youtube.com/watch?v=00_9JPltXHI