Close by issuer, isn't the end of the world, and is debatable if it will affect you in the future, but that may be the end of your relationship with American Express.
why wouldn't you care for this account? Do you have another account? Explain, why you wouldn't you care for this account? Is it under a fake identity or something?
First of all, this post was on behalf of a family member.
There is only one reason he opened this account (hint the same reason most people here open credit card accounts for

). Though there is no concern it will show on his credit report- it is a business account.
Interestingly enough, I tried helping out - this "concern" on the account was some kind of mix between a fraud and an FR, and no one in amex could fix it.
I personally once had amex close an account of mine because "they had determined after speaking to the real cardmember that the account opening was not authorized, I actually played them back my conversation on the phone with them clearly stating the opposite but they would not budge. That time though, it did not affect my ability to apply for more cards from amex (this was about 12 months ago).