I'm not arguing with you; it's just my perception that Amex has been better than the various Visas and MCs I've held.
Also, all purchases made with the card have their warranty doubled. So when my dell died right out of 2 yr warranty, I contacted them and was told to send it in. I then received a comparable unit from Dell the week after.
My Amex story is about getting fucked over in a legitimate transaction, and Amex making it right even though the problem had nothing to do with my credit card. I was told to expect this of Amex customer service, and they were right.
We had to buy full-price tickets (~ $1k) to get back home from a vacation due to a hurricane warning. We had no applicable insurance on original return tickets, but we got a full refund after a call to a bank's credit card department. Perhaps it wasn't 4 minutes as in your case, more like 15, but considering the circuimstances I think it's still pretty awesome :-)
It seems Amex is great as well I've just never had one of their cards.
I have absolutely the same experience with my bank's Visa.