Ive moved my 360 plenty of times while playing discs. Ive never had any scratches. Ive even had it knocked over by my dog in the middle of a fifa match. The game froze and i had to eject it and then put it back in but still no scratches.
Come to think of it, i also had it knocked over on hard wood floor. It got an error message and i freaked out. But i unplugged it and checked the disc, everything was still working fine afterwards.