I'm not sure what that vine is called, but I've seen mustang grapevines do the same thing -- growing roots two feet down from a severed trunk into the soil. That's obviously not a mustang grapevine. I thought I'm mention it though. Apparently, that's not so uncommon a survival technique.
The C. rhombifolia looks the closest from what I've seen so far. I think my leaves are thicker, more succulent, though.
I'll leave it open and investigate more. And I'll go check the ones in the back yard, see what's going on.