On Calypso's card, you see "NRA" member. It gives the landowner a familiar reference, but that's about it. I don't think if Calypso had a mishap the landowner could call the NRA and say hey one of your members just shot my cow, I want some money. I also don't think putting a reference to a website would help gain access anyway. Considering you didn't have to go to any safety classes, training, or have any credentials whatsoever to join, what advantage would the landowner see by allowing a member to hunt?
Although it's unlikely that any legal issues would arise, the liability is still greater than any benefit a member would get by being able to put the PM logo on a business card. You'd be much better off putting "references available" on it so that the landowner could check you out if he had any questions about your hunting qualifications and ethics.
Just two more cents for the pot.