I take the "Native American Horsemanship" concept about as seriously as I would if someone said they were Irish and did a "Celtic Horsemanship" method - which consisted of twirling stuff in horses' faces while the Riverdance soundtrack played in the background.
It's a gimmick, that's all it is. Just another "angle" for marketing basic horsemanship to an audience that wants it to be easy to follow.
The ironic thing is, so many people I've met who follow book/DVD programs are so anxious about whether or not they're doing things the way their chosen guru's program says to do them, they're not even paying attention to the way their own horse is responding.
They'd be much better off taking riding lessons with a qualified trainer, or finding a mentor in the area who can watch THEM work with THEIR horse and offer suggestions based on what they see happening.