Since when is there a limit on the AMEX black card? They don't give those cards out to just anybody!
I was glad that my credit card company watches unusual transactions. I once borrowed a large sum of money off my credit card and planned to pay it off before the next billing statement. When I got to the teller window at my bank to deposit the funds, my wife called saying the card company was on the phone asking if she had authorized the transaction. That was quick action on their part!