The best oranges [0] I've had were half green. Fresh from the tree, but still plenty ripe. It's my understanding that oranges for transport to colder countries are picked unripe and ripened in the holds of cargo ships. This ripening process is great at making the skin more orange, and OK at improving the flavour, but nowhere near as good for that as ripening on the tree. So if I saw green patches on my supermarket or…
That said, in the US, oranges destined for markets de-greened for aesthetic purposes since customers won't generally buy them otherwise.