Hmm. On further inspection it's because the HTML has a div containing a div. The outer div has the onmouseover setting, but under firefox, the inner div does not auto-propogate to the outer div any events it gets but doesn't want.
So the mouseover gets swallowed by Firefox except when your mouse is at the extremities of the region.
Turns out that the menu isn't actually Silverlight at all (just in a simmilar style), and that the Silverlight is entirely static and unappealing.
Someone should get their act together on this. It's a pretty poor show for new Silverlight developers.