Thats pretty much splitting the finest of hairs though. WDW is private property, but they don't prohibit anyone from coming on property. Your local shopping mall is private property. YEARS ago Disney did issue special transportation cards that you had to show the bus drivers - the last time I remember having one was in 1988, I think - it may have been before that though. 4 hotels, 2 themeparks - Disney was not the all encompassing beast it is now.
The fact is once you are on property you are a guest - whether its for parks or shopping or dining. If you want to go to a resort, or where ever for an afternoon/evening and wander around - you are free to do so on their transportation. Its not "public" transportation in that it only travels to Disney locations, but its certainly open to anyone who happens to be on Disney property for whatever reason.
Now WDW does connect to Orlando's public transportation. Lynx stops at TTC. If you didn't want to pay to park from off site you could take the bus in from 192/I-Drive and transfer at TTC. It doesn't really get much more public than that.
Transportation is for WDW Resort guests. If you have 1 foot on property somewhere - you are a WDW Resort guest. A bus driver has no business asking for any type of ID. I can stay at my mom's and come over to Ft. Wilderness for dinner anytime I want - no resort ID required, no theme park ticket required. Heck, my kids can go and ride the ponies - not even eat and its none of the bus drivers business.