Some say the theory is true, and some call B.S., but heres what my PERSONAL opinion is about running the claws backward...
From what I can tell, it makes sense to me to invert the contact patch of the chevrons on the softer terrain like we have here in Alaska. Running them forward they seem to be digging in with the pointed head of the tread first, and digging downward while kicking rocks, dirt, mud, snow, sand, etc out from under the tire, causing the vehicle to sink downward in the soil.
With them run the other way, I feel that it helps to create extra traction and flotation by having the tread act as "scoops", if you will, and they tend to pull the rocks, dirt, sand, snow, etc. into the center of the tread, and allow the vehicle to float up top better in the loose soil.
Like I said, some say its B.S., but I'm personally convinced and can feel a difference.
There were times when I'd be getting buried the further into a mudhole that I went and would lose forward momentum and progress... but eerily enough, I could back right out almost at Idle. So I flipped 'em. Seems to be helping.