He wasn't talking about our bill of rights in that statement. He was talking about the Soviet one. The presence of an independent judiciary in the Soviet Union would not have changed the fact that its BOR was an empty promise, because it had escape clauses a mile wide that assured that rights could not be exercised against what was purported to be the good of society. That's a direct consequence of the mentality that rights are granted by government, and we see that same mentality with regard to our own BOR. Just look at what's been done to the second amendment.
By the way, nothing in our Constitution says that only the courts can defend our rights. The foudners would have utterly rejected at such a notion, and so do I.