At some point, the Xbox has to vouch for whatever is connected to it.
I'm not sure that I buy that there couldn't be some manner of recording done via the Xbox; especially if it has a component output.
There's a whole lot more to something that modifies the video and/or audio stream than simply "passing through". Overlay is not a feature of today's HD video stream; the stream must be re-rendered with the goodies on it.
What do you mean by "vouch for whatever is connected to it"? It has to obey HDCP, just like a Directv receiver or Blu Ray player does. Whether the Xbox One or Blu Ray or Directv receiver or whatever, if there is an HDCP compliant device on the other end of its HDMI output, then it will output the content. If there is not, then it will refuse.
Think of the Xbox One as an AVC, just like some people have sitting between their Directv receiver and TV. It takes HDMI in, potentially does something to it, then outputs HDMI. So long as no copying takes place, it is free to send any HDCP protected content to its output (provided the device connected is HDCP compliant) It decrypts it to be able to alter it (overlay its own crap) then re-encrypts it again with its own HDCP key.
Of course you can potentially record what it outputs, in that respect it would be no different than whatever device it is getting its HDMI input from (Directv receiver, cable box, Blu Ray player) You don't even need component if you want to record an HD stream, there are some technically illegal (in the US, but not in other parts of the world) HDMI splitters that drop HDCP protection, and there are devices that will record an unprotected HDMI input. Between the two, you could record HBO off a Directv receiver's HDMI output if you wanted, despite the protection it intends to provide.
What do you mean by "overlay is not a feature of today's HD video stream"? First of all, HDMI is not a "video stream", it is a series of 1920x1080 bitmaps. MPEG4 is a video stream, but the MPEG4 has already been uncompressed prior to any bits getting to the Xbox One. It receives a single bitmap frame in 1/60th (for 720p or 1080p) or 1/30th (for 1080i) of a second and would be loading it into a buffer as it comes in. It can then change the value of any individual pixels as needed to overlay whatever graphics it likes before sending it via its HDMI output.
This is exactly what your TV does if you're watching something coming in its HDMI input and you hit the volume button and you see some graphics pop up on the screen for moment to tell you the volume is now 21. That's an overlay, just like what the Xbox One will do. There is no "rendering" involved. Since every TV I've ever seen that has an HDMI input (plus plenty in the days before HDMI came around) can do an overlay every time you hit volume, or menu or mute or whatever, I don't think the Xbox One is going to have any difficulty doing so.