You're not going insane.
In certain areas of the world you can find encounters with UFOs. If you see every UFO sighting you can fight the UFO on the cliffs near the Chocobo Forest place in Esthar (the one that's a forest inside a forest) and later meet Pupu at Balamb Island. Give him some Elixirs and he'll give you his card. If you like you can kill him, but I don't have the heart to.
