For starters - my 800 does not have the audio-enabled HDMI output. (Ie, I have VE12. Not VE12v2).
So, my 800 literally only (physically) connects via coax to my 861v6.
There is no physical connection relationship between 800 and HD621 in any way.
However, the 800 does have a HDMI video output and if you wish to view that output it should be connect to the HD621 so it can be switch to your screen.
If it's of no interest to you that's fine, but it's typically how 861/800/HD622 combinations are setup. (The only downside if there is one is it means another HDMI cable).
Out of curiosity have you never had cause to view the 800's HDMI video output?
Regards,
Carl