That's exacty correct. Property rights, so crucial to a free market and society are little more than a ruse anymore.
However a more insidious form of communism exists: government, always seeking power and therefore money may seek to take advantage of the prosperity of the free market. Government then operates under a false façade of ownership, alleging private property rights exist and doling them out in barely sufficient amounts as privileges in order to lure productive individuals to create wealth. This is properly called fascism.