I don't know about this one, dot. I think the use of the term "want" or "desire" can easily be said to rely on an appeal to forces outside of ones own control. The whole context of a situation that a discourse of "rights" or "desires" would emerge from sort of depends upon someone already not being treated, not doing, or not becoming or being what they want. It is interesting that you use such a blatant example of this by putting it in terms of a conversation about someone being hit and not wanting to be hit. If they don't have the capacity to prevent themselves from being hit without an appeal to something outside themselves, then whatever terminology they use to phrase the appeal to something outside their personal capacity is still an appeal. In this case, saying "I don't want you to hit me anymore" is an interpersonal example of a similar dynamic that is lame: an appeal to those with power over you to stop. What I think the concept of "Right" does is asserts a collective ethics. Of course it is bound up with a history of rights granted by the authority of the State, by Nature, by God, etc. But when it comes down to it, I think the discourse of "Right" is an antithetical discourse to that of Power. As to what form of Power "Right is derived from, that seems to be what the debate would benefit from being about.
[edit: adding more]
Actually, I think this is fundamental. Not necessarily the terminology, which I do agree with you could use some work. But, this whole topic of the way power is distributed or exercised in whatever sort of society we would want to consider. There's the concept of solidarity... and, when this concept is broken down in practice - solidarity is established based on some sort of shared ethic: why this person and not some other person is one to be in solidarity with (or these people and not those people). This though is different than Right(s). Right(s) are more particularized, more humanistic, and such. So there's this strange tension between "human rights" and "solidarity" and maybe the two play off of each other. For instance, let's say I believe every human being has a right to life so my solidarity with comrades ends when this right to life is not respected: the line that I will not cross. On the other hand, let's say that I believe the whole notion of human rights is bullshit so it is those who I specifically identify with that become the subject(s) of a collective ethic, and those that I do not identify with are subject to this ethic when is conflict with some other group or person.
Now here's where I think this becomes even more interesting. If I am a living participant in a commune and we consent to some basic ethics concerning conduct amongst each other, what do we call these ethics? Do we call them privileges, rights, rules, guidelines, principals of interaction, or what? In this context, they all seem to imply the same distribution of power and relationships among communards. How do you think about this and what are the relevant or significant aspects of these situations?