Can only be one of three things?
Pilot bearing - this spins all the time on the engine side, probably not this one
Throwout bearing - designed so when you push on the clutch pedal the bearing takes the load applied to the clutch via the pedal, I believe that even with the clutch released it is still spinning just not under a load.
Input Shaft Bearing(ISB) - This is the bearing input into the actual transmission, if the clutch is out (released) then the input shaft is spinning. Thus when you push in the clutch you disconnect the engine from the transmission so the input shaft stops rotating.
If yours is sounding just like the one in the video with the noise happening when clutch out and quiet when clutch pushed in then i have to go with most likely ISB. Now, I said most likely, I still wouldn't count out the clutch throw out bearing.
Either way any time you "pull" the transmission you should automatically replace both the pilot bearing and the clutch throw out bearing no questions asked. You have to seperate the transmission housing in order to get to the ISB bearing, not really that much more work since by then the transmission will be sitting on a bench.
Let us know what the dealer says!
Edit: Found this, has a nice diagrahm, they don't identify the pilot bearing but it will be located at the end of the shaft in the flywheel (black block on Lt) and the Input Shaft Bearing is out of the picture in the transmission off to the right.
http://auto.howstuffworks.com/clutch1.htm