Yes, I agree with you. There is no case here.
But at least we can go to HR to file formal complaint about the mistreated by the boss, cann't we? What the outcome is is really not an issue. But at least we make some voice. When the boss itemizes what you did wrong, he needs to provide evidence. ----I really don't know what the real world runs--- But is it worth doing that? For justice (is there really such thing in the world) ...how to fight back when the boss is unfair....