The medieval system was not merely hierarchical, it had independent subsystems of justice.
On this we disagree historically speaking, in as much as I say there was no medieval system of justice that can be particularly described as such.
I also do not agree that the church was not a super state. Using the argument of limited jurisdiction to say it was not a superstate, overlooks the fact that all governments throughout history have exercised limited jurisdiction to some degree or another. And so it was with the Church.
Your idea that "the Church... did not 'run' any states," is also not historically correct as you state it. Church lands, were quite often a state unto themselves, sometimes subordinate to other non church states, and sometimes completely independent of all other non church states.
Circumstantially, I can agree that the church you speak of "...was something similar to the system of universal rights that the libertarians hope to implement." Or at least many of them hope to implement. But such a notion at this time does not best describe libertarianism, as the considerations and options are far to numerous. It also implies a settled issue, that the libertarians have not even come close to settling.
The powerful and ardent pope, Gregory VII, sought in all earnestness to realize the Kingdom of God on earth under the guidance of the papacy. As successor of the Apostles of Christ, he claimed supreme authority in both spiritual and secular affairs. It seemed to this noble idealism that the successor of Peter could never act otherwise than according to the dictates of justice, goodness, and truth. In this spirit he claimed for the papacy supremacy over emperor, kings, and princes. But during the Middle Ages a rivalry had always existed between the popes and the emperors, twin representatives, so to speak, of authority. Henry III, the father of the young king, had even reduced the papacy to complete submission, a situation which Gregory now strove to reverse by crushing the imperial power and setting in its place the papacy. A long and bitter struggle was therefore unavoidable.In short, their was no system, only power plays.(Source: Conflict of Investitures)
That is a modern myth. It is impossible to read on the Middle Ages without constant reference to laws and covenants in effect at the time. It was a highly legalized society. But the point is not that both raw power and law existend in some kind of balance, just as today. The role of feudal proto-government -- the feudal lord -- was solely collective defense. Taxes levied by lay authority may have been high or low depending on many factors, but they went to support the only legitimate role of government -- defense of life and property, and delivery of justice. It was, particulalry in the early Middlel Ages, a direct trade of goods and labor for military protection.