I never watched that documentary, but from what I heard: The participants in the documentary went from an almost fast food only diet to a juice fast. So by default there would be health benefits gained.
I think it could be sound for simply losing weight, but:
1. How many calories consumed is a factor. I'm under the impression that there was some form of deifict.
2. The whole "Smoothie vs Juicing" debacle as to what is more nutritious. I personally don't buy the hype that juicing allows for nutrients to hit the body quicker (And is thusly better), but I'm also a smoothie fan due to the ease of it. So you don't have to listen to me.
This isn't to say that smoothies or juicing aren't a great supplement to one's diet/replacement for a meal or two, as well as helping those who have trouble eating certain fruits and vegetables. I'm planning to incorporate it into mine. With a better blender of course.