Your cousin is crazy. I know in the very old ages and mainly for very formal events it was custom to pay for your guest's travel but definetly not if it's a destination wedding. That would be absolutely outrageous. Show her the following page from the knot.com where it says you are not obligated. By the way this article talks about weddings in general so I would assume that it applies even more to a DW:
The Knot - Q&A: Wedding Guests: Should You Pay their Expenses?
"You're not obligated to pay your wedding guests' travel or hotel expenses. It is nice, however, to make it easier on guests by letting them know when your wedding will be as early as possible so they can start calling around for good airfares. You should also research hotels to see where you can get a good group rate; often, when a wedding party brings in a lot of guests, the hotel will give a discount to the group. You shouldn’t actually make the reservations, rather reserve a block of rooms, and then send your guests the hotel information they'll need along with the invitations. They should be given a reservation number, the nightly rate, as well as what to say when they call"