It's not a tube, it's an overground line. As evidenced by this Network Southeast livery.. on a tube train that's an overground train that goes entirely underground https://m.youtube.com/watch?v=MhUDyX4DKXQ
The Waterloo and City was transferred to London Underground in 1994, as part of the privatisation (or not in this case) of British Rail.
As the only way to get trains on and off the line involves craning them out of the depot[1], they did retain their Network South East livery for about a decade after formally becoming an Underground line though, until repainted at an off line overhaul.
[1] There used to be a lift that could take a carriage at a time to surface tracks, but the Eurostar extension at Waterloo did for that.
