why my birthday?

First Source Advantage has been calling me repeatedly for a month, asking for my birthdate. I never give it to them, because apparently they're trying to stick an unpaid American Express bill on me when it actually belongs to someone with a similar name. I've never had an Amex account, and confirmed with Amex directly that no one has opened an account in my name. First Source Advantage keeps calling, despite my repeatedly telling them that it's not my bill. They say they need my birthdate to confirm that it's not me, and that my birthdate is not personal information. Sounds fishy to me. Should I give them my birthdate, or will that just sink me deeper into their nonsense?