Yes, it really is a big problem, especially at the Contemporary which is walking distance to Magic Kingdom. They will tow your car if you leave it there more than 3 hours unless you have a Contemporary Hotel guest parking permit OR you have paid to have your car valet parked there. Otherwise, they will tow...too many people try to leave their car there for free & walk over to the MK. Obviously if that was allowed the lots at the monorail resorts would soon be full of non-paying customers leaving no room for the people who are legitimate hotel guest there. So yes, they are especially vigliant with the monorail & walking distance resorts. I'm sure you'll get some posts from folks who have never had a problem parking there, but just so you know it's a very real possibility.
We stayed at the Contemporary in Jan 2009 and even though the lot was more than 1/2 empty, they were towing cars both days we were there. We watched from our balcony. Three cars one day, two the next.