UPDATE Working fix as suggested by David (see below):
replace
$(\'.scrollMe\').bind(\"mousewheel DOMMouseScroll\", ...)
I can’t reproduce this bug in my FF 16.01 OSX using a touch pad (the Fiddle works fine), but I do know that there is another mozilla-specific event called MozMousePixelScroll. You might want to try to involve that as well.
There is also more information avail at MDN: https://developer.mozilla.org/en-US/docs/DOM/DOM_event_reference/DOMMouseScroll
As a sidenote, I think stopping the default action using e.preventDefault() should be enough, no need to stop the propagations as well (unless there are other IE specific bugs).