Beckles,
I suspect it was probably just a little more convenient or expedient, as well as providing CO with documentation, for the club to imprint your card rather than fill out your name and account number on a "sign-in" sheet. It's my understanding they receive a per person/usage reimbursement.
I think club access is one of the more useful perks that we have with our AMEX Platnium or Diners Club cards.