Card Member Services Robo calls to offer interest rate reduction on credit cards Atlanta Georgia

I get phone calls from "Card Member Services" about once per month  The calls are masked as it appears with a local number or Florida area code or other.  When you pick up the phone it is an automated message saying they can lower your interest rate.   I am on the National Do Not Call Registry. 

I had tried to stop these months ago and selected the option to talk to an agent and when I said I wanted them to stop calling me - I was hung up on.  Today, I tried again.  I had an agent with a very thick Indian accent.  I asked the name of the compnay and was told "Card Member Services" --- I asked him to confirm --- the name of your co is "Card Member Services" and he confirmed it was. 

I then asked where is your co headquarters and the response was they are headquarted in Atlanta, GA.    I asked his name and he told me it is "Harry Blaze"...... i asked him to spell it and he also gave me his company badge id, which i didn't make note of.   It just appeared that he was giving me false information, so i didn't pursue it.   

He asked me if i had a favorite credit card.   I told him it was Bank of America.    He asked for the last 4 digits of the account, which i gave him.    He put me on hold and came back with the correct account balance and my last payment amount and date.   I was shocked to learn that he had access to this information, but hopeful he did not have the full account number and card expiration date.    This is really scary...!!

He asked for other cards and i told him i didn't have any others.    He said he could see i had lots of other cards including an American Express card ending in xxxxxx.   I told him that if he had access to all of this information then, why would i need to give him the full account numbers and expiration dates?   He started getting pushy and asked why i was doubting what he was offering?   He continued asking for the Amex card number and date and which point i hung up on him.

I'm thinking that if i had given him the full account number and expire date, i would be seeing an unauthorized charge on my card shortly thereafter.