I believe that Dan et. al. are using "internal (not inner) power" to refer to a set of musculoskeletal causes and effects, that has little or nothing to do with one's mental or spiritual state. I could be wrong about that, so hopefully they will correct me if I am -- but I don't think they've claimed the term "inner power", and I'm pretty sure they haven't claimed any spiritual component as such.
in my experience of what Dan and others are doing, it has as much to do with the mental state, as the musculoskeletal condition/ing. As for these things being separate from a spiritual component, how can you have spiritual, without mind and body and vice versa?