I'm fairly positive the Concession Recovery Fee is a pass-through fee that all rental car companies charge at all airports as long as their location is on-site. Airport commissions consider rental car companies to be concessionaires at the airport and charge them a concession tax on all transactions which the companies then pass on to the customer. Below is a summary of the taxes and surcharges on a quote from National for a car at LAX:

Taxes, Surcharges and Fees
Customer Facility Charge $10.00
Concession Recoup Fee 10.60 Pct $22.33
Tourism Fee 3.5 Pct $7.37
Sales Tax (10.250%) $23.88
Subtotal $63.58

It looks as though National passes through less of the AP concession fee than Avis (10.6% to 11.1%), but charges a different sales tax rate, I haven't picked up a car at LAX in a few years, maybe the National lot is in a different ZIP code than the Avis lot?