You answered your own question. The legal bioses are linux based. The X3 is distributed with a legal BIOS - FlashBIOS, which is Linux based (source code is out there if you really want to look for it).
The illegal bioses are either developed using the Microsoft XDK (Xbox developer kit), or based on hacked version of the Microsoft BIOS.
But heres the kicker - all those "legal BIOS'" are capable of doing is running Linux (or technically running as a bootloader for linux). They can not run Xbox games. If you want to run games, you either need to disable the chip and run the stock MS BIOS - not a big deal, good for XBL, but not able to run games from you HDD - or you need to run an illegal BIOS in a second bank on the chip ... and which BIOS is commonly run? The Xecuter X2 BIOS or the Evox M8 BIOS - which are both illegal.