> The government's legitimacy comes from it's stick being bigger than yours

By the same argument, are Somalian warlords and Mexican drug cartel also legitimate in the territories they control? I don't think "legitimate" is the word you are looking for to describe pure power dynamics, since "legitimate" is imbued with a moralistic judgement (look up is vs ought etc.). But yes, in practice, if I have a gun pointed at my head, I could be forced to do things that go against my judgement (within limits!).