Amiga OS4 is based on Amiga OS source code, it is the natural evolution of AmigaOS on the PPC. Why it shouldn't be Amiga?
If we look at the OS4 featurelist, we read that everything is either completely rewritten from scratch or was never part of Amiga OS in the first place.
Exec - "completely rewritten and renamed"
Intuition - "OS4.0 sees a complete rewrite of intuition"
Graphics - "AmigaOS 4.0 includes a brand new font management system"
Audio - AHI (never part of AmigaOS until now)
Fonts - "Brand new font management system"
Filesystems - "Completely rewritten in C"
Amidock - "Complete rework"
TSP/IP stack - Completely new
AmigaInput - Completely new
Moovid and MUI - 3rd party addons
