I've dealt with very similar magazine scams before. They usually identify themselves only as "the people who send out your magazines", and pretend to connected with whoever might possibly  be sending you magazines (if you're even getting any, that is). They try to get your credit card number for a "discounted rate", or to "take you off the renewal list" or some such nonsense. One company even managed to buy my credit card number from somewhere, because they had it without me having to give it to them!

Bottom line, they're lying about you already having an account with them. If you complete the call with them, you'll find yourself signed up with an account, and that day will be the first recorded day of your account with them. Usually you can cancel within the first 3, or 5 or 7 days, depending on the company. If it's past that, file a complaint with the BBB and explain your situation. They've bailed me out a few times when I was really confused about why I supposedly had all these magazine accounts I never signed up for.