The same language appears under the Terms and Conditions for the Delta Reserve Amex:

Complimentary Access to The Centurion Lounge®

Delta SkyMiles® Reserve Basic and Additional Card Members receive complimentary access to The Centurion Lounge when flying on a same-day Delta-marketed or Delta-operated flight. The eligible flight must be booked on a U.S. issued American Express charge or credit Card. A Card Member may bring up to two guests at a per-visit rate of $50 per person, per location. Guests must be traveling on a same-day Delta-marketed or Delta-operated flight. Eligible lounges include all Centurion Lounges located in the United States, Hong Kong, and London.