I'm not sure that statement is totally true. (Unless they have changed/more strictly enforce policy). Back in 98, I was staying at an offsite hotel on International Drive using the hotel transportation and Mears.
(Hey it, was a free trip, beggars can't be choosy)
I soon discovered that I would not be able to go to the parks on my departure day and get back to my hotel for Mears to the airport without taking an expensive cab back to my hotel. So, I arranged my Mears to the airport from the Contemporary. I took the hotel shuttle to the Magic Kingdom and took my roller bag and bookbag with me. My roller bag was too big for the lockers, but they stored it in a room and gave me a claim check for it. They charged the same price as a large locker without the key deposit. When I left for the day, I picked up my bag, and took the monorail to the Contemporary, and caught Mears to the airport.
However, to the original poster, let the RAC desk and bell services handle your luggage on your last day!! Don't take it to the parks!! When staying at a Disney resort, that's the best way!!!!