You almost got it right. During the ratification debates the Federalists argued that a bill of rights was not only unnecessary but actually dangerous--that the existence of a list of areas where Congress was forbidden to legislate would imply that Congress was free to legislate in all other areas. And it was a valid argument, because that is one of the canons for judicial interpretation. So they included an amendment stating that the existence of the Bill of Rights didn't allow Congress to legislate beyond the areas enumerated in the Constitution. It's a companion amendment to the 10th. But I have to disagree that it allows the Supreme Court to recognize any fundamental rights not listed in the Bill of Rights or any of the following amendments. That is left to the citizens of the states, working through their own state legislatures and constitutions.
Well, the issue of what the Supreme Court was supposed to do is a fair point. The way the SCOTUS operates, it can find laws unconstitutional, and it finds what the common law is, interprets and applies statutes, and part of that is to determine the nature and extent of fundamental rights. However, of course, it was controversial at the time, until Marbury v Madison in 1803, whether the SCOTUS would be permitted to invalidate statutes.
As Thomas Jefferson wrote, "You seem … to consider the judges as ultimate arbiters of all constitutional questions; a very dangerous doctrine indeed, and one which would place us under the despotism of an oligarchy. … The Constitution has erected no such single tribunal."
Also, the idea of "fundamental rights" is interesting, in that the Constitution doesn't say there are "fundamental rights." What it does is say in the first amendment is "Congress shall make no law...." (expressly applying only to Congress, and not the President/Executive Branch or the Judicial Branch), or like the second amendment "...the right of the people to keep and bear arms shall not be infringed..." (which is broader in that it's worded in the passive voice, implying nobody can infringe that right). The third amendment declares that soldiers shall never be allowed to stay in people's houses without the owner's consent, except in time of war in accordance with a law passed by Congress. The fourth amendment refers to "the right of the people to be secure in their persons, houses, papers and effects from unreasonable searches and seizures. The fifth just and sixth says people aren't to be required to answer to capital/infamous crimes except on Grand Jury indictment, and that witnesses don't have to testify against themselves, confront witnesses against them, assistance of counsel, etc. The sixth talks of the right of accused to speedy and public trial, imipartial jury, not to be twice put in jeopardy of life or limb, and the right to due process of law. Seventh says that there is trial by jury for suits at common law, and eighth talks about no excessive bail.
Then nine says that the listing of those rights don't disparage other rights not listed -- so, that implies that there are other rights, not listed. And, ten says that any powers not delegated to the feds are left to the people and the States, but which powers to the people and which to the States are not specified, etc.
So, it's all very vague, and there is no "right of free speech" set forth - only a limitation on Congress not to make laws abridging "the freedom of speech."
After the Civil War, SCOTUS then used its assumed power under Marbury v. Madison to take the 14th Amendment due process clause, which said that states can't deprive someone of liberty, etc., without due process of law, and they said that what that means is States can't abridge the freedom of speech, religion, press, assembly, or commit unreasonable searches and seizures, deny people jury trials, etc.., except under rare circumstances, if any, thus adopting the "incorporation" doctrine. I never understood or accepted the rationale that the SCOTUS could just say that "you can't deprive people of liberty without due process of law" means that "a state faces the same restriction as Congress in not being allowed to abridge freedom of speech..." Don't get me wrong, I love freedom of speech, and I'm glad my State can't infringe on it either, but from an academic perspective, I don't think SCOTUS needed to "incorporate" (most of) the bill of rights into the 14th amendment to do so.