I get the same sequence of stops from that API link that the CSV has for route 53, run 2, albeit with northing/easting location instead of lat/long.
(I'm extremely sceptical about the 11m minimum distance too - having done the entire 53 route a few times, I can't remember any stops that are basically on top of each other.)
[-0.126102, 51.502769] to [-0.126018, 51.502714]
What is happening is that the TfL sequence API is starting the bus route sequence on one side of the road of Parliament Street, before turning it around at the corner with Whitehall Place. The bus stops on either side of the road are very close together. Other maps/sequences elsewhere start the sequence at the end of Parliament Street, meaning the short distance is avoided.
[1] `.stopPointSequences | .[0] | .stopPoint | .[] | [.name, .id, (.lat|tostring), (.lon|tostring)]` in jq parlance
I guess the 389/631 routes are reasonably simple and don't need more "drawing points" than you'd get from the bus stops anyway?
[edit: added the 389 bus stops and line points to the imgur gallery]