The last time that happened to me, collections took one look at the notes on the account, apologised, informed me that his manager was now writing an extremely annoyed email to billing, and had it fixed before I was off the phone.
Collections tend to be more likely to play hardball, but they often also tend to contain smarter humans. Sometimes this helps.
I did this once, and was impressed with how intelligent, friendly, and helpful the collections agency was.
Unfortunately, billing responded to the collections agency by yanking the debt back from that collections agency and referring it to another, meaning I had to start all over again. I don't know if that's against the rules, but it didn't seem fair and certainly wasn't nice.
Collections tend to be more likely to play hardball, but they often also tend to contain smarter humans. Sometimes this helps.