I'm not very good at debate, but I'll give this a shot. Hammond leased Isla Nublar from the Costa Rican government. The reason he says "I own an island..." is probably because it sounds better, and then he would go into further detail later. To prepare for this answer, I looked it up on the Isla Nublar movie canon page on Wikia, and this is pretty much how they explain this. I own an island probably just sounds better than I leased an island, since not everyone knows what a lease is, so it would probably confuse the general movie audience.
stormy_lass from Jurassic Park Legacy