Can Bank of America Do This?

I closed my checking acct with a zero bal. at the end of the month & this month receive a bank statement showing (- $37.50) in my account. I was surprised because I had to go to a special employee who closes accts. Today I find out after but after speaking with the 3rd tier supervisor, my account was never closed due to a coding error & there was a $10.00 automatic payment made on my behalf (in which the bank said I should be grateful to them for making it) However since it was their mistake they will happily refund all the charges except for the $10.00. I told them without any money in my acct and the acct closed they shouldn't have paid the creditor and it was their mistake & that they should reverse all the charges. She told me that I should have called my creditor & tell them to stop billing them. If I do not pay the $10 in 160 days they will send me to their collections dept. My credit is great! can they mess up my credit with this. It is not the money it is principal