Re: Can we finally just accept that these are PCs in all but name now?
I can't comment on newer Xbox consoles, but you pretty much had full control over the original Xbox. You could even show a static image while you rebooted the machine (which took a fraction of a second) - I know of at least one game that did that after each level. (Not my responsibility, but it was a game I worked on.)
On the Xbox360 DirectX was a super thin layer on top of the hardware (the API wasn't even implemented as proper COM interfaces), and the OS was basically a cut down XP kernel which ran on a single hardware thread on a single CPU core. The compiler didn't even support C++ exceptions properly - they were that focused on performance (support was buggy from when we first got our hands on alpha hardware (basically beefed up Apple Power Macs) and we were told that it would never be fixed).
I'd be very surprised if they'd changed those things. (Well, I guess the compiler is better these days now there are x86 processors under the hood.)