Yeah, christep... When I talk about the "private" shuttles, what i mean is that they are not really franchised "public" ones like the 3 bus companies. The distinction is indeed very small.
The MTR/Airport Express is run by the MTRC, a government owned "corporation". Same as the KCRC, which runs the KCR East, KCR West and the LRT.
Running public transport is a lucrative business, as the goverment almost guarantees a 15% yield, or else they can apply for fare increases. Also being in the private sector, and no ridiculous yearly almost-guaranteed pay raises (until the last year or so) of government employees, the pay of bus drivers, etc are much lower than they are in say, the US.
And the service of those companies really weren't that good until the late 80's. I grew up there, so I know about waiting for a long time for a packed bus. Things are so so so much better now.