'Setting man free from men' implies 'setting every man free from any mans power'.
Mens power, even in a private society, is not guaranteed to be equal among the people.
Therefore some people will not be free from other peoples power, even in a private world.
Maybe they could be free from a legitimate power, but not from power.
You could say one maybe deserves his power, in a private society.
But, deserving power means there is either an objective or subjective scale to measure when someone does.
If it's subjective, a man or a group of man has the power to decide. Therefore we are all ruled from this ideas, and we are not free.
If it's objective, maybe not everybody considers it objective. This is enough to have at least one person that is experiencing being subject to someone elses power (this could be, for istance, me).
And this is enough to say a society of privacy is not enough to set man free from men.
Also, if bitcoin was private, it wont be worth a dollar right now.