Did you read the state.gov page? The CBP (US Customs) website says the same thing.
But you need a real passport to enter Caribbean countries other than Bermuda. And cruise ships: A valid passport is required for all international itineraries including Africa, Asia, Australia and New Zealand, Europe, India, Central and South America, Panama Canal (partial and full transit), Caribbean voyages that visit Martinique or Guadeloupe, South Pacific, Tahiti and World Cruises. Although US and Canadian passport holders are not currently required to sail with a passport on domestic itineraries (including Alaska, Bermuda, Canada, Caribbean, Hawaii, and Mexico),