This is true. When you try to use the warranty from the credit card, you're working with a third party insurance company. You can get it done, but it's not painless.
I have a similar protection deal that comes with my VISA card, and the way the contract reads is I just pay for the repair myself through Apple or whatever, then I send VISA the receipt and they reimburse me. There is nothing in the wording that I have seen about dealing with any third party at all.