Wait... do they even recognize themselves as independent? I thought they were in "free association" or something with New Zealand.
They do! The US is far from the first country to establish diplomatic relations with the Cook Islands and Niue. However, the 3 countries in free association with the US are UN members, while the 2 in free association with NZ are not. The reason for this difference seems to be that Niueans and Cook Islanders have NZ citizenship, and NZ may stop granting them citizenship if they take that additional step. Meanwhile, countries in free association with the US have separate citizenship, but it grants them access to many of the same programs and protections within the US as US citizens have.