I am trying to find a clip of a no pivot step. Here is discussion on it on bullshido:
http://www.bullshido.net/forums/site...30078-p-4.html
several of them were taught not to pivot also. It is also mentioned in there that bas rutten and cro cop are propoents of not pivoting. I was taught that by a dutch guy, so it kinda falls in line.
EDIT: skimming over it, that is actually a decent thread - they talk about the cross being a common counter, about the arm swing and foot placement. I'm not registered on the site, so I can't see the vids and pics, but the discussion itself is good.