Your comment is either extremely naive or terribly disingenuous. Even in the XXI century we see nations invested in annexation campaigns motivated by their need to reach military and strategic objectives. There are even nations that are deeply invested in creating artificial islands much like Diego Garcia to achieve goals that are achieved by Diego Garcia. Why can anyone talk about self determination if nothing stops an occupier from simply dropping anchor and taking over the place?
There's plenty of land left on the island where these people can live, they're not demanding independence or that the military base have to leave.
My comment was made in the context that even if the BIOT were to become independent, this doesn't sound like a big deal for the military base. It's very likely that if that were to happen the US could simply offer them the same deal that the independent Marshall Islands and two other island republics have:
https://en.wikipedia.org/wiki/Compact_of_Free_Association#Mi...
Your statement is similarly silly. The issue in question is whether the islanders can return & have the right to self-determination.
There's no reason the US & UK couldn't work out some deal with them to continue having a military presence on the islands, the US has bases in plenty of sovereign countries, e.g. Germany.