Life on top:
Think of it this way. Up to the flat rated temperature, the engine is able to produce its stated rated thrust.
Now, a TOGA departure at 4C will achieve the same thrust as one at 30C
HOWEVER the engine will be using less fuel to achieve that same thrust. In other words there will be no performance difference - simply a lower EGT at the lower temperature.
When using assumed temp. methods then there will be a "density margin" as you point out. So, by my reasoning that will only apply for the range above the flat rated temperature.
Note: we are only talking about engine performance here!
As a historical footnote - on the B707 with JT3D (no FADEC) engines we had approval to operate the engines at HIGHER than rated thrust in limited circumstances. ie. the F/E over EPR'd the engines to achieve extra thrust. This was at the expense of engine life. Only used departing Nairobi.