Late Supreme Court Justice Antonin Scalia refutes the notion that the United States are such a free country because of the Bill of Rights:
But then I tell them, if you think that the Bill of Rights is what sets us apart, you are crazy. Every banana republic has a bill of rights. Every president for life has a bill of rights. The bill of rights of the former evil empire, the Union of Soviet Socialist Republics, was much better than ours. I mean that literally. It was much better. We guarantee freedom of speech and of the press. Big deal. They guaranteed freedom of speech, of the press, of street demonstrations and protests, and anyone who is caught trying to suppress criticism of the government will be called to account. Whoa, that is wonderful stuff.
He then goes on explaining that what sets America apart is the structure of its government with checks and balances that make sure no one can amass too much power.
Full transcript on govinfo.