"Paleo"-fitness sounds backward to me. All my ancestors are gone. What matters is my life, here and now. I am a human of today's world.
"Run for your life". Could be jump, crawl, climb, swim, fight etc,... for your life. Moving naturally will make you feel strongly ALIVE.
On the subject of MovNat etc, Naeem, in a testimonial from one of his clients, has some excellent thoughts on movement : Testimonial - Iron Man Cédric Hénaux