David - I just missed this call, and yes "Heather from Account Services" is a scam. Do not give these people any real information. Feel free to waste their time with fake information, though!
What they do, from what I can determine from talking to them, is to call your credit card company and ask for a lower rate (which you can do yourself, but they probably lie about stuff to get them to agree). If they get a interest rate reduction, they charge your card for some amount in relation to the amount of reduced interest you would pay (i.e. save $1000 in interest for X years, they charge you $500). But since they charge that to your card, you're paying interest in that money, too, so it's probably not really saving you anything - and you're paying them for the privilege.
That's why they want to get enough information from you so they can look up your bank statement - which I guess they call your bank and use the info you give them to social engineer that - i.e. they've asked for the last 4 of my social, as well as 16 digit card number and expiration date. They've also asked before if I knew what my card limit was, so they are looking for account with enough room in your limit to charge your card for their "service".
(No, I didn't give them any real information, I google "fake name generator" and fed them info from that.)