So any person at all that comes into your home he is fine with - it's only out on walks?
Your above story doesn't seem so bad either...he didn't hurt the other dog, doesn't sound like he was mean at all to the woman (who was quite unkind to him!), and stopped immediately.
So far, he really doesn't seem that bad (but then I'd say I have the king of all reactive dogs).
By any chance, have you been able to establish if his reactivity is fear or frustration based? That would be helpful to know.
I'm not saying balanced is bad, really, because there are a lot of people who seem to think that positive training is primarily +R and won't entertain any of the other quadrants. The only quadrant that I would absolutely stay away from, personally, is +P (my exception being natural consequences....for example, dog bothers chicken, dog gets pecked, etc.).
Anyway, I'd definitely talk to this new trainer about what he thinks the core issue is, and what his plans are to remedy it. I'd also do a lot of research on reactivity yourself (if you haven't already). Read some of the stickies here, not just the reactivity one. This one is pretty good:
http://www.dogforum.com/training-behavior-stickies/suppression-modification-shutdown-fallout-4776/
The thing with reactivity and balanced training,
especially with fear reactivity is that +P methods will make it much worse in the long run. Many will think the problem can be "solved" by punishing the behavior, but it does nothing to solve the underlying fear which will pop up eventually and often more severely. The behavioral modifications promoted here, like DS/CC, LAT, BAT, may take more time and not feel as "satisfying" but they do work if utilized appropriately.
Anyway...my main point is, ask him and analyze his methods. If it seems like something that is going to scare, upset, or hurt your dog - don't do it. I worked with a vet who claimed to specialize in behavior cases who wanted me to pen my dog in a corner of a room where he couldn't escape and just wait for him to stop barking. No. That would be an example of shut down and would be massively stressful.
Best of luck.