That is correct, but privilege also has its origin in the preamble of the Constitution. The Supreme Court has recognized...and there is the legislative codification of privilege that talks about those privileges that existed in the U.K. in 1867 and so on. However, there are also the inherent privileges from the preamble of the Constitution, and those are based on necessity, what's needed for parliaments and houses to operate.
At the core of that is control over proceedings in Parliament and internal proceedings. There is no question about the the existence of that privilege and that autonomy for the House to make its own determinations about how it's going to operate within the confines of other provisions of the Constitution.