I tried that, I think, when I was messing around with this using FireBug.
But the result was the pop-up tooltip was then "hidden"... down below the taskbar button. I could only see a few pixels of the top edge of it. Sure, that stopped the scroll bar from appearing (I think, anyway, not sure now since I don't remember exactly IF it worked) but the result still wasn't right, since it meant the tooltip didn't show anymore.
But maybe overflow:hidden applied to a different element would work, I'm just not sure what to apply it to...
-JC
P.S. Again, this is fine in later versions of FireFox, so I dunno if it's worth tracking down. Not sure where in the progress from FireFox 3.X to current 24+ "gawd knows what number FF version they're up to now" it was that it got fixed however...