True, but cultures that don't have modern fire tech have many methods of building fire that most modern Western people won't be able to do. Think bow drills, hand drills, fire plows, etc. A lot of city folks don't know how to even select wood, much less prepare it in a way that will allow them to successfully build fire even with matches or a lighter! I've seen folks at campgrounds that can't get a fire going easily even with a can of lighter fluid.

Fun topic! It would be hard to pick the items without knowing more about the island. If it was an island in Alaska then shelter and fire tools would be high priorities to me. But on some equatorial islands there may be high enough temps to not really need fire and of course no suitable wood to build a fire to begin with. In a situation on the latter type of island a reverse osmosis desalinator would be very useful!

Just off the cuff I'd say a tent, mirror, matches and flare gun would be pretty handing in any situation. If there is wood to burn then the flare gun would be a bit less important.