To my knowledge, no USA-issued credit card includes Liability insurance.
If your American Express card is issued in the USA, it provides only Collision Damage Waiver. This means it covers damage to the rental car itself. It does not cover damage to any other car or property. It does not cover injury to any person. If you have personal auto insurance that policy provides your primary coverage against all of these risks, and the American Express benefit is secondary for CDW only.
This is clearly disclosed on the American Express website:
This product provides secondary coverage. This means it pays eligible benefits not paid by any primary insurance that you have. This product provides collision damage to the rented vehicle but does not cover such things as damages to other vehicles or property.
https://www.americanexpress.com/us/c...nce-terms.html