To be clear, I enrolled online and never heard back from Equinox. Then I went into a club and they had no problems enrolling me under the Centurion program which is integrated in the Equinox system. But they did type my card number into their system which could perhaps do a database lookup at Amex or from a list that Amex sent them. And they checked my ID to see it match the name on the card.

And in the Equinox app it shows my membership level as "Amex Destination Access"