What are you now--Elmer Fudd?
Yellow Cab and Greyhound are for profit corporations.
Of course they are. They're still public transportation. Your error is
noted.
Amtrak, Metropolitan Transit Authority (NYC), and Chicago Transit
Authority are public and are subsidized.
I've just given you a couple of examples which are public and not
subsidized.
I'd have to get up pretty late in the morning to be corrected by the
World's Greatest DXer.