I'd been meaning to respond on this.
I think Theater View DOES have background video support. There was something...
It certainly does NOT pull them down automagically from somewhere on the Internets like the automatic image slideshow does (as was pointed out above, where would it get them and how could you control the quality?), but... I think there is something where you can customize the Theater View skin, or put videos into some magic folders or something, and then it'll use them instead of the automatic slideshow.
Not really what I think the OP was asking for, but I don't know how they'd do that (there's no massive, curated repository of silent background videos organized by artist anywhere -- certainly not a free one that has a nice API that JRiver could use). But, if you wanted to do something yourself, I think there are some tools available.