No one. They've been separated from the world for ages. They never cared about others, just wanted to live they lives. When a british group found the island, in the 40s, they accepted them because the group itself didn't want to reveal the existance of the island.
Besides, I'm pretty sure the inhabitants don't even know what countries are out there. They know something about 5 or 6 continents and world wars and whatnot from the british men tales, but nothing more. They're quite an introverted population.
Before I forget - I've heard of oil companies drilling (or trying to drill) in the Arctic. So if you wanted them to use oil/gas as a resource, you could.
I think you have some flexibility on this independence issue. Do you want other nations to be trying to declare sovereignty over the island? It could be a subplot, or you could probably write an entire novel over it. If one nation (for example, Russia) wants to declare sovereignty, there's a good chance other nations (like the US, Britain, etc.) will throw their hats in the ring, just because they don't want Russia to get more power.
On the other hand, I've heard of some tribes in the Amazon who have little or no contact with the "outside world". Even Japan was extremely isolated until the 1850s. If this island is truly lacking in resources (except for the flora and fauna that
might be useful), then maybe no one cares. Or, rather, the rest of the world is happy with the status quo (the island being independent) and would only become involved if another nation is trying to take away their independence.