Saying that reusing the Linux kernel is the same as being "just another Linux distribution" is the problem: most Linux distributions are just Unix clone: if you create a VMS, a BeOS, a MacOS or Plan9 with a Linux kernel then what you have is a different OS with a Linux kernel not just a Unix clone.
Using the Linux kernel doesn't force you to be POSIX compatible (which is a double edged sword: you get a lot of software but you loose your "originality").