There are buses from the Ticket and Transportation Center to any place you need to go, so I would assume that you can just hop on a bus and go. I've never had to show resort ID to get on one. I've never had to show resort ID for any of the transportation ferries, monorail, etc.
But it is true that you can't park at a resort and go on a bus. You have to stay at the resort to park there. I know going into the All-Star Resort section they do check ID, so I think it's the same at all the resorts. Some will even check to see if you have a dining reservation if that's what you're parking at the resort for.