I am familiar with the system. What it is really addressing is the average outstanding balance. By using the HELOC approach you are able to immediately pay down a debt. So irregardless of the interest rate you are lowering the average outstanding balance of money so this is helping to pay down the debt early.
I get what they are doing. It is sort of like a diet plan. I think a lot of them are good but you have to be able to follow them and be disciplined. Additionally a lot of people who fall off diets get fatter afterwards.