"Natural Horsemanship" is just an advertising gimmick. After all, nobody advertises "Un-Natural Horsemanship practiced here!!" and if you claimed "Conventional Horsemanship" people would think you were going to beat and torture the horse into submission.
I'd suggest pretending you don't see "Natural Horsemanship" and interview trainers the same as you would if none of them claimed that. Ask around for references.... people are MORE than happy to talk for hours about trainers that did a great job with their horses. Ask at Tack Shops, ask your Vet, heck you can even post on Craigslist asking folks for references an listen to what they have to say. When 20 people come back and say the exact skills a trainer taught their horse and how happy they are, that's what you want vs 3 people yapping about how their horse came back and is now their BFF Forever and gives cuddles, hugs and would never ever squash them into the ground because they have the bestest bond in the whole world!