IMO, the only time having another card really holds any bearing is when you can shuffle limits in order to open a new account. Otherwise, it's fairly irrelevant. You are asking to open an SPG card and being judged on the standards of that card.
Now, on a manual review, a rep can obviously see your existing account and maybe it will give you another chance but computers don't manually review things, which is why recon can sometimes be a help. That said, Amex is very rarely known to overturn the computer's decision.
