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.
Of course, there are musculoskeletal causes and effects, but it has everything to do with your mental state. If you believe Ueshiba then it has everything to do with your spiritual state as well...