I don't think Amex have a single worldwide policy.
The policy is specific to each card issuing country. You need to get a copy of the policy for the country where your card is issued, and read that policy in detail.

As example. For UK, the Amex car rental coverage is provided so long as the rental is in the card holder's name - the coverage for UK does extend to also cover anyone else who is a named driver on the rental documents (but they must be named on the rental documents)

Rules for your coverage may well be different - you really do have to read the policy document.