And I agree with you on the second part: everyone agrees the sky is blue and that grass is green. But the fuzzy edges are what kills it and I don't think you can define it rigorously except by drawing some arbitrary lines on the color wheel. Which will be just that: arbitrary
Why? Everything has fuzzy edges. If you think fuzzy edges are fatal you won't be able to communicate about anything in the real world.
Thanks for the reference, but it's not really what you claimed. It's not that they don't have a word for "green", it's that they don't have separate words for "green" and "blue", so they use the same word for both. That is not quite the same as not having a word for "green".
You can see the same phenomenon in English. We have separate words for "orange" and "brown" even though they are actually the same hue just with different luminosities. Brown is just a dark orange.
That's news to me. Reference?
BTW, the word "green" just means something different when applied to eyes than when applied to everything else. And green is a continuum so there is some fuzz around the edges. But if the task is to pick out green from a palate of half a dozen canonical colors I can definitely build a machine to do it with >99% accuracy.