Yes, anyone can ride Disney transportation, not just those staying onsite. The website and other sources touting free transportation are merely Disney marketing gimmicks. They never say the transportation is available ONLY to onsite guests.
Yes, that's the intent, but in practice it's not even that restrictive. A legitimate use without a park ticket might be parking at DTD, doing some shopping, then taking the boat to Port Orleans or the bus to Grand Floridian for dinner, then returning to see Cirque.
Heck, someone with a public transportation fetish could ride the busses, boats, and monorail all day long without purchasing theme park admission.
Jim