This is not the first time the BR symbol has been missed off FH.
I agree that maybe there are longer term plans for some (all?) southern trains to run on the middle fast track between sydenham and new cross gate. (The points are already there.)

1. This would reduce interference between the 2 services.
(explains how a regular service will better integrate with the more random southern service).

2. It would also encourage passengers going into london from these Overground-only stations to stay on the train at NXG and take the longer route. Which is the main point of the exercise, after all.
(explains why they think the overground will be a popular route in).

3. It would make the Southern service faster for their premium customers from further out.

So it makes sense.
They would also need to discourage passengers taking a short-cut back home, via charring cross/waterloo/LB/NXG -perhaps by making many of the evening Southern services fast to norwood junction... (another piece of the jigsaw...).

Incidentally, I had not realised that restrictions to london bridge due to competing franchises had been played out before:

wiki link

There were plans to run this line all the way to charring cross! You can still see where this now disused line branched away underneath south bermondsey station.gmaps link