No, that ain't right. I live in a town where we all know who's who in the business community, that would not be worth the damages it would cause. Afterall integrity, in life, as well as business, is all we have.
I actually had something similar happen a couple years back. I took out a line of credit for 50K. Two weeks later the bank sent me a form saying the debt had been retired!?! I had already spent almost all of it, and had definitely not paid it back at that point. It took me almost three months to convince the bank of it's error. In those three months I got two more letters confirming the debt was paid. Both my accountant and my lawyer said I should give up on telling the bank and just file those letters away figuring the bank would someday come looking for their money. At that point I would have to pay it back, but not any interest that accrued in the meantime. I couldn't do that.