I want to add that it's not unprecedented for Parliament to determine some circumscription of their parliamentary privilege. The Parliamentary Protective Service legislation that was recently passed was another example of something whereby, from a parliamentary privilege standpoint, the Speakers would have been vested with that exclusive power, and it would have been one of their parliamentary privileges. They ceded some of that power to put together the parliamentary precinct service. This, then, is not atypical of an ability to circumscribe parliamentary privilege.
On November 29th, 2016. See this statement in context.