If I have something showing 'awaiting collection' at my PO Box it means it is too big for the box or a signature is required.

Either way I have to use my key to get the card out of the box and present it at the counter to get my goods. No card, no item. Except if the boss is there, probably. We've known each other for a lot longer than I've had the PO Box.

Bottom line, anything sent to a PO Box can only be collected by the owner of the box or an authorised representative.

I wouldn't call the buyer a liar, but maybe, as said, check with AP. And if he opens a dispute, fall back on seller protection.