The agent doesn't require "proof" of the number if you, for whatever reason, only decide to put the number in at check-in.

You can show an old boarding pass, or a slip of paper that you have jotted it down on, or the card stored in the wallet on your phone, or just recite the number.

If the number is of the wrong format, it won't go in. The miles can, anyway, be retro-claimed.

If the number is wrong, you won't get the miles. The miles can, anyway, be retro-claimed.

Being able to put your number into the booking is not sufficient justification for issuing a plastic/physical card.