It's not double counting, it's a simple method to arrive at the finance fee without using complex formulas. This makes calculating rent charges for leasing much easier than those for loans, which use a more complex formula. The money factor takes into account the addition, so don't panic. To get the equivalent APR interest rate, multiply the money factor by 2400. This is where the similarity between leases and loans ends.
Loans use a complex formula for interest, and some calculators can figure out loan payments.
Now here's the difference. Rent charge uses the Finance Fee formula above. With leasing, you don't need a business calculator to figure out the rent charge, just one that can add and multiply. It won't help you make payments still owed to the leasing company. Gap insurance covers the gap, between the value of your car and the amount you still owe on your lease, including a possible penalty for early termination of the lease.