The rules mention on page 5: "Place the Privilege card facedown in front of you. The Privilege card remains secret...".
This must become: "Show the Privilege card. The target card of the Privilege card remains secret as long as ..."
When playing a Claim/Exchange Privilege card, you must ALWAYS wait to reveal the Gift, Keep or Discard card until the Gift card is accepted.
Otherwise, the player who is offered the Gift card, has extra information to accept Gift card or not.