You are correct that there are also cases where use is clearly commercial. Simply selling the licensed work is one although I expect the sort of person who does that doesn't really care much about the license.

Another is probably things like advertising but if the organization has any sort of legal department, they're probably going to want to confirm that you have rights to the work in question.

And then, as I say, there's a vast middle ground about which different people have differing strong opinions.