Is this mortgage advice good, or is it hooey?
That makes no sense at all. They try to compare and that's exactly the same as comparing apples versus oranges. Mortgage is long-term loan, so for the first many years the huge part of the payment will go to repaying interest, so that ratio 1 will indeed be something like 20% or more despite the fact that the interest rate on the mortgage is much lower - something around 6%. HELOC will have the interest rate of 6%, but it will have the same structure so that you have equal payments, so if you compute that ratio 1 it will be very close to that of the mortgage. The bottom line is - if HELOCs were that great noone would apply for mortgages. You should stick to making extra payments towards the principal on the mortgage.