If Aruba, Curacao and the BVIs are in this ...

[Rogin the Armchair fan]

Why don't England, Wales, Scotland and Northern Ireland compete as separate teams?

[Discordant Resonance]

NI athletes can elect to compete for either Ireland or GB depending on preference, as the McIlroy saga demonstrated. It seems the IOC takes the same approach as UEFA to national affiliations, as previously, a National Committee didn't have belong to a sovereign state, but since 1996, they have to be a UN member, with the previous teams allowed to remain.

[Southport Zeb]

In 1908 six teams entered the hockey tournament - France, Germany and the four home nations. The two continental sides were eliminated in the first round, with England going on to beat Ireland 8-1 in the final. Scotland and Wales were both awarded bronze medals as losing semi finalists. In the official record all four medals are classed as having been won by Great Britain.

[Satchmo Distel]

I think countries that aren't independent states, such as Aruba and Puerto Rico can compete provided they had Olympic Committees before the IOC changed the rules. Curacao does not have an Olympic Committee so its athletes compete for the Netherlands according to Wiki. Sometimes athletes compete as independent individuals if their nation has just become independent but the Olympic Committee has not yet been formed, e.g. South Sudan in 2012.