It might seem a pedantic difference, but that does not entail that that central authority has rights, or at least not an unconditional right to exist. One could say a group of people have a right to organize in such a way that there is a central authority IF they do not break some set of rules, like that group of people must have a morally sound claim to the territory they're going to administer, they must not use that authority to harm others without justification, so on and so forth. The 'rights' of the authority are entirely dependent on the rights of the people organizing and using it. Simply stating "Israel has a right to exist" is begging the question in a technical sense. It's refusing to engage with the qualifications necessary to morally justify authority and simply stating that that authority is legitimate without justification.