It is incumbent upon them under the law to prove that the debt exists and that you owe it, and that they have the legal right to collect it.  You are not obligated under the law to prove that you don’t owe or that it is paid.

Federal law (FDCPA) requires them to send you a letter (US MAIL ONLY) postmarked within 5 days of their first contact that contains their name, physical address, the creditor’s name, and the amount of the alleged debt.  It also must contains “mini-Miranda” telling you that it is an attempt to collect a debt and that all information will be used for those purposes.  The one other important thing that this letter must also have in it is that you have a right to dispute the debt within 30 days of receipt of the letter and if you do so, all collection activity must be stopped until the debt is verified.

Read up on your rights here and also make a complaint at this government site:  http://www.consumerfinance.gov/

Also file a complaint with your State Attorney General's office.
List of State AG’s offices:   http://800notes.com/faq/attorney-general