Yep. The airline will almost certainly want you to have the credit card used to purchase the ticket to verify that you're "authorized" to claim the ticket, and

Yep. The airline will almost certainly want you to have the credit card used to purchase the ticket to verify that you're "authorized" to claim the ticket, and the TSA will give you the third degree at the checkpoint, but -because the airlines are common carriers- you cannot be required to present ID to fly.