FE Hoppy:Because the thrust scheduled at actual and assumed is the same and therefore the N1 required to achieve that thrust is the same.
Sorry to bang on about this however - reference to Villas's link pages 7 & 10
suggest that the density issue is not fully factored out by the FADEC. Boeing say that there is in fact more thrust produced at the assumed temp. than would be at the actual higher temp. This I think is what the OP was after.
So, the "density" issue with respect to the engine thrust would be from the actual lower ambient temp rather than the top of the flat rate?
PS Keith Williams or Old Smokie please feel free to intervene!!