No, you are mixing up the State's Statute of Limitations and the CRA's allocated reporting time. Two different situations.
By paying on an old debt yes it does start the states statute of limitation ( of how long they can legally sue you in your state) but since you've paid it off in full it makes it a moot point
The Credit Reporting Agencies will keep on for 7 and half years of you DOFD whether or not you've paid, are paying or going to pay in the future. once it has reached 7.5 years it should automatically fall off.