Yes, I was told firsthand by the Amex Credit Reporting Dept that it is their standard practice to report the open date of any subsequent accounts as the same year as the first account you had with them.
Just be prepared to prove you actually had the old account in case they can't find your old account in their system. The fact that you have an account from them on your credit report is not enough to convince them. They will want the full account number of the old account.
My first Amex was opened in 1994, but they can't find any record of it, so my card reports 2007. Thirteen years of free history would have been nice.