The hierarchy isn't so much about how green each individual option is, but rather about how trips should be distributed to reach an overall optimum.

For short trips or connections, walking should be more convenient because you don't need any gear or space to store your bike. This also gives a multiplicative effect with other transport options, because (e.g.) people are much more likely to take a bus or train if they can walk directly to the station instead of needing a bike or car to get there in the first place.

As an aside, mature bicycle infrastructure goes beyond bike lanes, especially as the number of cyclists grows. For instance, here's a video showing off a huge bicycle parking facility in Amsterdam: https://youtu.be/EqwasBTzZS8?t=530. Obviously this is great compared to car parking, but it's still a lot compared to the infrastructure needed to support short walking trips.