The strong presumption with the use of parliamentary privilege is that one's career is curtailed in one way or another if it is invoked to tell an untruth.

You are right that this suggestion is in opposition to that, in some ways, but it's also worth noting that the way not to be prosecuted is to continue with the strong presumption that lying to parliament is bad.

In practice this law would be more about official communications aimed at the press, where in the recent election we have seen the former government side engage in some pretty egregious lying without consequence, including misusing the work of non-partisan civil service functions.