Seems somewhat similar to the Josh Barnett "catch wrestling" submission style. Like Roy said a couple of posts up, IMO many Brazilian HW submission artists are coming from a pure BJJ background.
When Mir and Barnett were growing up in the USA, BJJ was not that popular here at that time. I'd throw a young Jeff Monson into that group.
It just seems like they were among the first US HW's on board seriously focusing on submissions.
That said, again IMO, the Brazilian HW submission artists are far more comfortable working from the bottom that you Mir's, Barnetts and Monsons who basically adjusted their overall grappling styles to give them the best opportunity to work from the top.