Egad, I’m a long-winded bastard. Maybe I should change my name to NanoEsq. 
Still, I promised to address the OP, so I will.
I do not believe that legal positivism is a correct way of viewing how we do or should govern ourselves. The general idea of positivism, as I understand it, is that knowledge should be based on empirically verifiable naturally observable phenomena. In this framework, metaphisical and theological theories are meaningless, since they draw on non-observable data to reach conclusions. For instance, positivism would declare meaningless a theory that the Earth was at the center of the Universe if that theory was based on theological arguments; it would only accept empirical data to determine if, indeed, the Earth were at the center. If it could not be determined, then it would be considered unsolvable until better data were available. Logical positivism carries this a step further: it considers only analytically or conclusively verifiable statements as meaningful. As I understand this, a positivist would consider a theory about the beginning of the Universe meaningful only to the extent that it could be verified by observational data; the story of the Bible wouldn’t be considered ‘knowledge’.
There is, of course, difficulty with attempting to apply a theory for dealing with observational data about natural phenomena to human relations and the concept of government. I think you can imagine the difficulty that would arise injecting positivism into a dispute between a believer in devine creation of man and a believer in the *** of man; each would loudly assert that HIS theory was supported by the ‘evidence’ and that the other theory relied on inferences and guesswork; each would, of course, totally ingore the fact that the answer to the ultimate question cannot ever be determined by empiric data, there having been no contemporary human witness. Even more difficult is the application of such logic to a study of ‘rights’, ‘privileges’ and duties.
Let us, then, start with the concept of a ‘right’. It is this concept that underlies almost the entire structure of our plan of government. Everyone can quote the famous line from our Declaration of Independence: “that they are endowed by their Creator with certain inalienable rights, that among these are life, liberty and the pursuit of happiness.” They belong to you and me and no stinking government can take them away! Would that this were true.
If we define a ‘right’ as something intrinsic to a human, that cannot be prevented by act of man or nature, then humans have no ‘rights’. As I think Robert Heinlein pointed out in his book, Starship Troopers, what right to life does a drowning man have? Can he appeal to God or Mother Nature and protest that he will die? Does it stop murderers from killing? Accidental and intentional death are a part of the fabric of life; and even if you avoid those, eventually the flesh gives up the ghost and you die. Where, then, your valued ‘right’?
But the fathers of the country weren’t talking about ‘rights’ in that sense. The ‘right’ that they are talking about is the expectation that they will be allowed certain things by their fellow men. When men act to constrain a man depriving him of certain things, that is, in their view, inherently wrong. When government restricts my liberty, it should do so not by whim, but by a need, a need so great it outweighs my ‘right’ to be free from such interference.
The fathers also saw ‘rights’ as something that government couldn’t grant to its citizens, but rather something inherent in people that they could not abridge by creating a social compact to govern themselves. Unlike England, where the King was the viewed as the source of the power to govern, and could grant to his people ‘rights’, these men envisioned that people had the right to govern, and that when man establishes a government for himself, he doesn’t yield up certain basic things to which he is justly entitled. This view was, of course, totally inconsistent with monarchial government; it lead inevitably to conflict with the other viewpoint.
Now, viewed even this way, can we establish that a ‘right’ is something intrinsic? Can we engage in some sort of search for empirical evidence to indicate to what things a man is entitled at all times justly? Can we see it? Hear it? Taste it? Smell it? Touch it? Of course not. In the truest sense, positivism is meaningless in dealing with such inquiries.
But let’s go beyond positivism in the truest sense. Can we somehow logically deduce those things to which man is entitled, those things he needs, and those things which he should do as a duty?
Make a statment of a hypothesis about a ‘right’ man has. Begin to defend that statement with logic. I defy you to reach any conclusion about the statement without reference to some value system, some set of mores. The right to life? Oh, please, does a man really have a right to life if his ‘right’ interferes with a substantial need of society and society doesn’t view the individual as important? Suppose my society consists of people who are living in intolerably crowded conditions, and continued procreation would potentially result in privation for the culture. Suppose that such a culture does not value individual life, except as it can contribute to society as a whole. For such a culture, does the individual have a logical ‘right’ to live? Similar examples exist for privilege, duty, etc.
You state that, for the record, you “support full rights for every citizen.” What do you mean by this? Do you support the right of such a citizen to pollute, despite the fact it will impact his fellow citizens? Do you support his right to treat animals cruelly, because he perceives a need to do so for his own economic gain? Do you consider that he should never be incarcerated, never be limited in his liberties, never be registered, lisenced, imposed upon by the government in any way? Does he have the right to bear an AK-47? Does he have the right to use said AK-47 to avoid the imposition of governmental authority he views as violative of his rights? Does he have the right to perform an abortion? To abort his child? To NOT be aborted while still in the womb?
Do you view fundamental Islamic governments as inherently improper, because they treat individuals differently from how our founding fathers believed should be done? Do you consider caning, removal of hands, stoning to be ‘barbaric’ and a deprivation of ‘rights’? Do you feel that no one should be killed, even when condemned to death by a government for crimes committed? Is war ever justifiable, or should the U.S. simply lay down its arms and admit that, by shooting at enemies, it violates their ‘right’ to life and liberty?
If you want to understand exactly how the idea of legal positivism fails, I invite you to apply its principles to the debate about abortion. If you can manage to successfully conclude what the law regarding abortion should be in all societies, without reference to any belief system about what life is or what the individual’s worth is, then accept legal positivism as having a value. I am fairly certain this attempt will fail, as it has failed to allow us to resolve this debate.
Our country was founded on the basis of certain assumptions about what the fundamental tenets of government were. We have not substantially changed those tenets in over 200 years, but we do modify their application to the challenge each new generation faces. We base our tenets on the mores and beliefs of our people, as expressed democratically. There are no intrinsically correct laws; laws are the creation of man to weave the fabric of his mores around himself, and to repair the rents in that fabric whenever they occur.