A long time ago when I was about 19 or 20 I worked for a collection agency. We had contracts with various companies ranging from Hydro companies to credit card companies (capital one specifically).
Anyway our calls actually sounded a lot like that....what we were asking for was a "cheque/pmt by phone" as opposed to having the card holder mail it or pay online. Reason for this was we were actually measured based on how many payments over the phone we got. In order to get this pmt over the phone we would need the branch number, etc. etc. (#'s found on your cheque).
Occassionaly we would have people with pretty good credit end up in our system for like a $20 balance on their card which was only a week or two past due. Those were the worst because you end up feeling like a prick for even calling about it lol
Anyway even though I did that job and it was legit, if someone was ever to call me asking for the same thing because I was behind I'd still pay online lol Better safe than sorry
Last point - never get a job at a collection agency it is the most depressing job as a teenager/young adult i ever had haha