Absolutely not a fan of Project Veritas and its rogue, lawless, strange ways, but I do have to say they may have a point if the documents were leaked by the FBI.
Imagine if a law enforcement agency carrying out a lawful search in support of a possible criminal prosecution, was then able to circumvent attorney/client privilege, by simply leaking the documents to a news organization who can in turn claim that freedom of the press trumps attorney/client privilege, thereby destroying it. It's especially icky when, as in this case, the attorney/client privilege seems to related to ...criminal prosecution. And while you're right that the attorney/client privilege isn't spelled out in the constitution, it's arguably at least related to the Sixth Amendment right to counsel. So I don't know. I think Project Veritas sucks, I think getting a personal diary of a President's child sucks, I think they manipulate facts and I feel icky even sort of coming to their defense. But there is a lot of tail wagging the dog here if a law enforcement agency can have a news organization destroy attorney/client privilege.
It would feel different if the leak came from within Project Veritas, because then arguably the attorney/client privilege had been waived.
But it's something we'll never know. Fascinating piece.