A tui is a native bird of New Zealand and is (to the best of my knowledge) not found anywhere else. It was also known as a "Parsons bird" due to the white tuft making it look like a "vicar".

They used to be very rare around the suburbs of Wellington until they built a predator proof fence around Wellington's old water reserviour site (near Karori) and made a bird santuary in the midst of the city. An absolutely terrific idea and if you are ever in Wellington I highly recommend a trip there, tui, kaka and now they even have a few Tuatara (lizards species as old as dinosaurs) as well.

But as the link from the OP suggested people (in a noisey city) are complaining about the noise of a few birds. Pretty funny and stupid really. Plus to complain the ring the sanctuary to complain - like they are the sanctuary's pets!!

As for Kea they are not a huge problem (like monkeys can be) as there are not that many of them and their habitat is pretty limited and does not really overlap with people apart from on ski fields etc. They are up there as one of the coolest animals on the planet - just for sheer personality.