Oh, for sure that's the reason. What just makes it funny to me is that because of this, you can also drop by the island again later for free infinite tent farming.I'm guessing it was developer foresight in case the players came in with no tents to initiate the cutscene. The scene itself happens when you lay down a tent to recover, so the players dying with no way to get a tent if they forgot to bring any would break the game. They just didn't feel like changing the variables after that, so that island only has that one encounter with that one drop.
Granted tents only cost like 500 gil so by this point in the game they really aren't much of an expense, but still.