Well, I like Onkyo receivers. They're what I've always bought. IMO the 7xx series is and always has been the sweet spot of the lineup. The main virtue of the 875 is the video processing chip and while it may very well do a bettter job with scaling than your cable box, I personally don't consider that too big of a deal.
If the video camera is playing the audio, there may be a setting to change to have it pass the audio to the TV. There is a lot of handshaking, exchanging of keys, and feature negotiation going on with HDMI so it's also possible that with the TV speakers off, the TV is responding 'not supported' for audio and the camera defaults to taking care of the audio. In your case, a receiver with 4 HDMI inputs (a true 'repeater' receiver like the higher numbered Onkyos and many others) would make it simpler but if the video camera isn't used all that much, another alternative would be an external HDMI switch.