The resorts with direct access to parks (Polynesian, GF, CR, BW, YC/BC) all have signage up that states that parking is not provided for park access. What is so hard to understand? If you aren't staying at that resort, but are enjoying the facilities in some way, and then want to head to a park afterwards, then pay to valet park. I have asked at almost all of those resorts and been told that valet parking is fine if you want to head to a park...self parking is not. More than a few hours and it's for resort guests.
Have I been towed? No. But, I have seen tow trucks in the CR and Polynesian lots...on several occasions.
And if it's really busy, such as Christmas, July 4th, you may find that only resort guests are allowed to valet park!