It does not have to harm your credit rating. You are right make them prove it. Look up "debt validation letter" and send them one (hurry up, you have 30 days from when they first sent you a letter) . Send it registered. Once you you have conformation they got it pull your credit report (annualcreditreport.com). If they are reporting it contest it with the credit reporting agencies.
If they validate the debt on your credit report without sending you validation of the debt you can sue them.