Yeah, but their trip away from the island was planned on a raft, not in a ship.

Anyway, if you didn't pick it up from the game, or my previous post here, Sora and the others didn't actually live on the island (well, maybe Wakka, Tidus, and Selphie did). First, Sora looks outside to see the island in a storm, then when he returns, he exclaims "Riku's boat! And Kairi's!?" (somethin' like that).
I didn't pick that up on my first play through. I used to think that they lived on the island itself. I also thought that they didn't have parents, until you hear Sora's mom call for him for dinner (or did she tell him to go to sleep? I can't remember), and Riku saying that they may never see their parents again.