Just to clarify...
If you drive your <i><b>own</b></i> car (and your rental car is considered your own car), you drive right up to the terminal to drop off your bags.
But if take third-party transportation (a shuttle van, a towncar service, etc.) they will drop you and your luggage off at a point somewhere in the parking lot. But don't worry, it's a short walk from that drop-off point to the terminal, and you won't have to haul your luggage... they'll take over once you've dropped your luggage at that dropoff point.