These protections have only been provided under statute for positions that the government characterizes as agents of Parliament, so the Information Commissioner, Privacy Commissioner, for example, as well as the...under Bill C-2 there's also been a proposal to provide the same types of authorities for the Auditor General.
The government has not proposed to add these to the Public Service Commission under Bill C-2, as the Public Service Commission is not included or characterized by the government as being an agent of Parliament because it carries out executive functions.