I think everyone broadly agrees that rights are justified claims and liberties, but exactly how they are justified will differ greatly from person to person, but the discussion at hand is quite compatible with a broad range of justification, so there is no particular need to disambiguate it.
It also came into my mind, that there are two kinds of libertarians -- there are those for whom property is a consequence of justice, and those for whom property is the foundation of justice. I think Gavagai is trying to work out for himself a position of the latter sort, but a commitment to such a position makes any argument against a particular allocation of property on justice or fairness grounds simply impossible. In fact, that's largely the point of such a stance, I think.
It also came into my mind, that there are two kinds of libertarians -- there are those for whom property is a consequence of justice, and those for whom property is the foundation of justice. I think Gavagai is trying to work out for himself a position of the latter sort, but a commitment to such a position makes any argument against a particular allocation of property on justice or fairness grounds simply impossible. In fact, that's largely the point of such a stance, I think.