My educated guess as an attorney is that the debtor would need to prove he / she paid the debt in full, but I have never seen this issue before so it is legally interesting. If it went to court it may even be a case of who the judge believes, but in all likelihood there is a statute somewhere on this. I agree with Sly that the best course is old bank records. They are there on some microfiche somewhere.
I have 2 basic policies when it comes to loaning money or covering a debt of any kind: 1) Know who I'm lending to 2) Only loan what I'm willing to lose
Thanks for the comments. I came to the same conclusion most of you did, that the debtor has to show proof that it was paid in full. I think the LA Times article linked is a little different than this situation because Verizon apparently wasn't able to offer proof that the debt ever existed, it just claimed it existed. Here, the creditor can prove the total debt existed and has at least some kind of record that a partial payment was paid, but there's no evidence that it was ever paid in full. The debtor is just claiming it was.