The Constitution does not purport to give rights to anybody. It declares that certain things are rights and prohibits the US government from violating them.

You're confusing the declaration of independence, a fluff document, with the Constitution, a legal document. Fluffy language aside, in the Anglo-American tradition, rights derive from legal documents (or precedents), and the right to habeas corpus or a jury trial derives from the Constitution and is circumscribed the the territorial jurisdiction of the Constitution.