Assuming that you want the processor to be able to cope with digital audio coming in over HDMI, you've only got two choices: either the processor has to be able to take audio and video on its input and pass through the video (which would probably require additional digital video circuitry to be added, although I'm not sure - adding an OSD certainly would!)
Thanks Nicolasb. And so we come to the heart of my question: Isn't the HDMI signal just a data transmission protocol? Purely digital in nature? If this is so then it isn't a video signal and passing it through the processor would offer none of the risks of degradation (an "analog" video signal would have) to audio quality.
And if this is so it really doesn't matter if the signal is passed through the SP. The digital video signal would be converted into analog at the TV end, or possible the Video switcher, depending on what it does to the signal.
This is what I always assumed anyways, so I don't see the need to enforce the "audio only" criteria for the SP on the HDMI signal.

I just assumed they would pass the signal through the SP, process it and pass the signal containing the video out again.
Please feel free to correct me if any of my assumptions are wrong.