Leaking and Motivation
The government are trying to open up a completely new argument in respect of the arrest of Damian Green.
They are trying to approach it from the perspective that the motivation of the leaker matters.
The point about parliamentary privilege is that communicating with an MP is privileged meaning that it cannot be criminal to talk to an MP. If it cannot be criminal then it does not matter what the motivation is.
The way they government are trying to take the debate would lead to a code of conduct for moles who would not be allowed to accept even a cup of tea from the leakees.
Preventing opposition politicians from using leaked information is a massive undermining of democracy.
It is the same issue with whistleblowing anywhere. It is important to protect whistleblowers from suffering as a result of whistleblowing. The government's argument is that whistleblowers must never benefit from whistleblowing.
You can have it one way or the other.