Companies do not necessarily need DOB or SSN to report to the credit bureaus. A matching name and address can be enough. That is one of the reasons that inaccurate information is sometimes posted to reports. If I understand your situation correctly then you apparently closed the payment account (checking) before all the payments were made?
If that is the case then their reporting of a derogatory information would be legal and correct. Under the Fair Credit Reporting Act they were obligated to send you a notice regarding this information within 5 days of their action. Did you perhaps also move during this timeframe? Even if the notice did not reach you it does not mean that the debt is in error. I would suggest that you take a trip over to the Rebuilding Your Credit forum and read up on what to do with collection accounts.
You will need to start with a debt validation (DV) letter to these folks and then hopefully work out a pay for delete (PFD) to remove the item from your report. If you cannot get it removed it is going to remain for at least seven years from the original default date. And if it is not already assigned to a collection agency you could get further negative reporting on your report. Good luck in your quest to handle this. Most of us have recovered from much bigger mistakes than one account gone bad.