You should never hit a bird full stop. This could seriously injure the bird and if anything cause it to bite more.
Since we cannot communicate feelings back and forth via words to out pets it is important that we take the time needed to read their body language, as they read ours. Individuals show their emotions in different ways, and unless the bird has been raised by its parents and its parents were raised by their parents and so on… then it might not show the usual body language for its species, or it might, it really depends on the individual. Anyway most birds bite (and I mean proper bite) because 1 there in pain, 2 they are scared, 3 they are aggressive/angry at you or 4 its how they think they should react. Basicaly its allways to do with the person/owners thats there/raised them, other than ofcourse your bird is injured through a totaly unpredicted accident and it takes the vets/nurses/your finger off… then come on its noones fault… poor bird!
But yeah all birds bite in some way shape or form, if you watch a fully bonded pair of macaws for instance when threatening the person (at the time me! lol) they often bite each others beaks, not hard enough to hurt each other but hard enough to be glad that its not my hand! lol However the hand reared macaw that hates all other birds (but likes snakes???) saw this and tried it on his favourite person next time they got close enough (again me!) and lets say having a macaw hanging of your lip after seeing that display of power is a bit worrying but lucky for me he ignored my nerves and did it just enough to show his stength without hurting me. Like you said they use their beaks to communicate with each other in the wild and as wild animals still use it in captivity.