You are right, but I am, too :-). In my mind, a taxi also is public transportation. I do not think I am alone in that. Wikipedia disagrees with it in http://en.wikipedia.org/wiki/Public_transport ("as distinct from modes such as taxicab"), but http://en.wikipedia.org/wiki/Taxicab talks of "modes of public transport" for taxicabs. I guess the terminology will become more confused if/when driverless cars become commonplace.