That isn't entirely true...if the owner of the debt (whether or not it is the original owner) decides to delete it from the credit record, then they can. In fact, many debt buyers act this way - they buy the debt for pennies on the dollar, and then offer to delete it if the person pays, for example, 25% of the amount owed. As mentioned elsewhere, this is know as PFD or "Pay for Delete".

Most of the major credit bureaus require that you own the debt of 5,000 or more people before they will accept payment history records and/or delete requests from the debt owner. That's the only restriction.