Modern consoles that play videos need to rely on some form of an OS. For a company such as Sony or Nintendo to "reinvent the wheel" by writing a new OS from scratch every time a new console is being developed seems to be a waste of resources. I'm not mentioning mikrosoft since they have Windows to use as a base for Xbox.
By using something like Debian, Arch, RHEL, game companies can save time by not having to write a new OS all over again. The only issue I can see with this approach is that any modified GPL licensed code would have to be re-released under the same license and it seems that big companies are not fond of the GPL for that reason (to keep any changes to the original code private).
Anywho, these vast array of distributions and frameworks nowadays make it silly for Sony or Nintendo to start from scratch every time they want to make a new console.
Note: This thread is getting so many replies. Uh, thanks. But WOW, this is interesting.