Yes, I'm aware of that approach.

It's likely tougher than it seems; the big important bits that the news will care about have to match up when checked, and anyone with high-level access to this stuff likely has a significantly sized staff who also has access to it. Paraphrasing reduces the chance of some minute detail tweak being included in the reporting at all.

You also have to actively expect and plan to do it in advance, which takes a lot of labor, time, and chances of people comparing notes and saying "what the fuck, we're being tested". You can't canary trap after the leak.