The argument goes that those items you mentioned don't grant rights, they recognize pre-existing rights already given to us by some deity, and they are actually restrictions on government so that government doesn't deny us these pre-existing rights.
Amendment #6
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.
It’s hard not to read this as a right defined by the bill.