Yes, the same theory that bothers the DEP's Parks Division about liability could apply to the five towns through the CLA. Also, the state law for landowner liability release for hunters, trappers, fishermen and anyone else given written permission to use private lands by the landowner only applies if the land use is free. If you charge then under Ct. statute you are not protected from liability. That is another reason the DEP charges only for parking, not "useage" because their own state statutes creates for them a liability if they charge for use. So the CLA incurs this liability for the five towns by charging a useage sticker.
By the way, the DEP has been relatively silent on the whole issue but internally there are divisions that are against the sticker program for many reasons. It is not something they would initiate.