That is true. But irrelevant. Read the rest of the founding documents. The Constitution says what it says because it encoded the founder's best attempt at setting up a government that acted according to their shared philosophy of governance. This philosophy included the notion that "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

Read your history. The BoR was controversial at its time of adoption. One of the arguments against the adoption of the BoR was that these rights existed before the government was founded, and were indeed inalienable. Some were worried that, should they encode this limited set of rights to text, other rights not so enumerated would be usurped.

How right they were.

Or, as I posted earlier, just read the 2008 Heller decision. The Supremes therein baldly state that rights exist separate from the Constitution. The Constitution cannot usurp a right that is inalienable.