by questioning them publicly and holding them to account. That's not a leak. That's keeping people in check (or force them to lie in front of camera). Remove that and you only rely on Edward Snowdens of the world.
My understanding is they want off-the-record information from unnamed sources. These aren't public questions like at a press conference. Those can still occur under the current rules.
If they publish off-the-record information without approval of authorities, they will no longer be accredited to attend press conferences. Of course no self-respecting reporter is going to accept this - if you do, next step is "if you publish lies about our president, you will not be accredited" - trust me, I know, this is how it starts.