All the information needs to be exactly the same on the accounts - phone number, mailing address, permanent address, etc. I called in to Citibank when I got the AA card and they sorted it out for me - but it was kind of a huge mess because they had to look at my other records and match them and there was probably some more security stuff etc.
You must have gotten a rep who didn't feel like going through the trouble. Try again! You might let them know that the information might be different on the two accounts.