I don't see why this should be so hard. They could use Google Maps to do the walking path and then just apply a default walking speed (or even let you set yours) to calculate walking time.
Google Maps doesn't do depth or man-made obstructions to walking. The bus he's trying to catch is directly on top of the underground station, leading a simplistic walk estimator to give a near-instantaneous result. In actuality there are multiple stairs as well as a bottleneck-prone exit gate.
