Moving a server while it's serving

We're having an argument over here, which we need you to settle. One member of my team says that if you move a server (we have Dell PowerEdges) while it's on and running (like, say, you pull the server rack over 2 feet) you may damage the disk drives. Therefore, he claims we need to shut off every single one of our servers to move the rack 2 feet. Another of our team says that's ridiculous, and that we should be able to slide our rack 2 feet over on the carpet without compromising the integrity of the disk drives.  I say that maybe I should stop using my computer as a foot rest if this is true.

So is this fact? Urban legend? Possible, but a 1/1000 chance?

Our having to stay until 10:00 tonight depends on your answer!