As long as people aren't literally (i.e. biologically) colour-blind, then all the colours exist, whether you have a name for them or not. The question, though, is how—if you have a name for them—that affects how well you distinguish them from other colours.

With Berlin & Kay, given that (like you) I don't know most of the languages they cite, I can't say how much their source material was affected by the mother tongue of the sociologists and linguists doing the research they drew on. One thing stuck out like a sore thumb, though. When they dealt with languages that had more basic colour terms than either Berlin or Kay themselves, they immediately had real doubt about it. Because of course no language could have more basic colour terms than English!