OK, this is one of the WTFs one could expect from IE.
I took a file from the livedemo, saved it as html, and started removing chumks from it. When I was left with only 2 style definitions, and a button, I started removing the remaining possibilities..and the result it:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
makes IE buttons get properly skinned. *sigh*