CDs are pretty rugged, and the error-correcting codes they use can handle lots of scratches and dings. I have read that CDs are dishwasher safe, and if they can handle that they certainly can handle a few fingerprints!
But it is a "better safe than sorry" sort of thing. Keeping your fingers off of the CD reduces oil and dust, which helps keep the laser and motor inside the drive clean.
Here are some interesting links:
Here are some places to buy music CDs: