It's a view consistent with the Preamble to the same, which stated that it was passed "to prevent misconstruction or abuse of its [the Constitution's] powers", which would mean federal powers, since the states don't get their powers from the U.S. Constitution. It's also consistent with the reason why the BOR was passed: namely, because the people were afraid that this new federal experiment would be too large and too distant to be controlled by them. They weren't looking for protection from their own state governments. You'll notice that the Articles of Confederation didn't contain a bill of rights. It was only after the Constitution was passed that the people demanded one.