The mention of safety due to lack of doors does not add up, as none of the Routemaster busses at the time had a door at the bottom of the stairs. Jumping on and off was the normal thing.
The many tunnels under the Thames are awesome though - I used to live in Woolwich and there’s a pedestrian tunnel there that I’ve used many times
But you could jump off at any speed - or get jostled and fall off accidentally if hanging on to the pole that was provided in the doorway. Falling into traffic at 30mph isn’t a bundle of laughs either
My guess is the door requirement was to avoid needing to scrape people off the single lane roadway in rush hour more than a thought for passenger safety and that difference may have got lost on the way to the page
The many tunnels under the Thames are awesome though - I used to live in Woolwich and there’s a pedestrian tunnel there that I’ve used many times