I see this from time to time as well. I think it is more than a coincidence now regarding when it happens though. Although it makes NO sense to me, I see it specifically after I have remove the Wii Sports disk, and attempt to play something else. Nearly 100% of the time, the next disk inserted will click\whir whatever, and give the message on screen to power down etc. Things work fine after that.
Again, makes no sense to me, but it does seem to happen. On a side note on the same issue, if I remove the Wii Sports disk, power off the machine, turn it back on again, and THEN insert another game disk, the problem does not appear. Strange.