So typical of them to lie
Collection agencies have really earned their bad reputation. They are trying to collect money no matter what, and are simply lying to you.
They also like to create a false pretence of urgency, saying that the offer is only valid today, or this week. They try to put pressure on people so they can’t think straight and don’t have enough time to find out their real rights.
The truth is that all derogatory items age off your credit report 7-1/2 years from date of first deficiency (default). It makes no difference whether the debt is paid, settled, or unpaid (See how-long-do-negative-items-stay-on-my-credit-report.html for a complete list). This is per the FCRA and nothing restarts that clock.
If you have debts on your credit report that show up after that 7-1/2 year period, simply dispute them with the credit bureaus as being too old.