You'll also note that I qualified "antiquated" in my original post with "a bit." Many of those things have been fixed by amendments (13, 14, 15, and 19, for example).
You are, of course, correct that the Consitution does not create our freedoms, but merely protects them. However, this is again simply a matter of semantics. A government that does not protect freedoms can be seen as not granting them, and a government that does protect freedoms can be seen as providing them. My point stands.
P.S. Our freedoms may be inherent, but that doesn't mean they come from a deity. =)