IANAL but I believe the law says if the journalist didn't aid in whatever made obtaining it illegal, like hacking the data out, then they are clear to publish it. And that's what one Dem called for Twitter to write in its policy, according to the "Twitter files":
Twitter never shut down Wikileaks or other things in the interest of national security that involved civilians and government officials alike. They have allowed journalists to leak other similar stories from hacks constantly. The Panama Papers, etc were all mostly civilians. Twitter never censored that, except in China at the behest of the CCP. Which comes to the original point. No politician or political arm should have the power or influence to take something down they find unfavorable. I prefer not to live in a CCP like state where the "party" gets an edit button on everyone's thoughts.
Then they can flag the offending post through twitter's reporting system like everyone else