I think that's exactly what will happen.

When a competent journalist gets a leaked document, they'll learn to only summarize it, but won't quote it verbatim or duplicate it. That'll circumvent and kind of passive leak-detection system that could reveal their source.

Then the only thing that would reveal the source is if the authority starts telling suspected leakers entirely different things, to see what gets out.

Then you fix that loophole by subtlety altering the phrasing or formatting that you send everyone