In the end, it's not Chuck who punches a journalist, but Raleigh.
There's lots of video footage of the event, including what caused Raleigh to lash out. They're in Los Angeles, just coming out of the TV station where the night's live show just ended, and the path to the car is lined with eager fans and sensation hungry reporters. Raleigh and Chuck take the time to interact with fans and reporters just like they've been instructed to do. They've been doing a good job of it until they happen to come across a guy in a black polo shirt with the World Press logo printed over the breast pocket. The World Press is not exactly known for serious news, but for the steady string of gossip they provide - never mind if it's rumours, truth or totally fake - and the reporter is quite obviously one of the rather unpleasantly tenacious individuals the World Press likes to employ.
Stacker watches the scene play out on the screen of his tablet with a sense of dread forming in his stomach. He just received notice of the event and is currently reviewing the footage. He can see things turning bad even before they do. The World Press reporter has absolutely no sense for what is appropriate and he's obviously out to provoke a reaction from the Rangers. He doesn't have any sense of self-preservation either, considering that he chose Chuck Hansen as part of his target practise. Chuck has never been known to suffer fools gladly, and even less for holding back when provoked. His reputation as a volatile character is known to every journalist, as far as Stacker is aware. So that man should have known better.
The reporter shoots one inappropriate question after the other at Chuck and Raleigh, some aimed at their part in Operation Pitfall, some at their personal life, some at their recently revealed status as a couple. They both give one or two measured answers, otherwise they ignore him. For a moment Stacker thinks that maybe they'll just walk off, but then he hears the reporter shout at Raleigh: "If you had the choice, who would you pick to survive: your brother or Chuck Hansen?"
Raleigh doesn't even hesitate, his reaction is so immediate that Stacker doubts even Chuck could have prevented it. One quick punch to the guy's nose that obviously breaks under the impact and then the reporter is on the ground on his knees, his hand clasped over his bloody nose. It takes him only a second to recover, then the man is shouting obscenities at Raleigh, inarticulate due to his broken nose. Raleigh snarls at him, then he turns and leaves, his steps fast and clipped. He's obviously fighting for control so that he doesn't hit the guy again.
In the background Naomi Sokolov is visible from the camera's angle, watching her colleague with crossed arms and making no attempt to help him. She can be heard saying, "I told you not to ask that specific question" with an unforgiving tone in her voice. Somehow Stacker gets the feeling there's a story behind that sentence that he's not privy to.
Interestingly enough, though, Raleigh's transgression doesn't result in any bad press. Quite to the contrary, actually. Of course it's all over social media and the news-outlets within hours and makes the international headlines the next morning. Stacker expected things along the lines of "Jaeger pilot punches journalist" or "PPDC violence against civilians" or maybe even "PPDC attempts to intimidate the press". He's quite surprised that's not the case, though. People are actually on Raleigh's side and comments make it clear that not only do they think that the reporter was completely out of line, but also that he deserved what he got. It certainly helped that several serious reporters witnessed the entire scene firsthand and hold not too much sympathy for their offensive colleague.
And while Stacker can't condone violence against civilians, in this specific case he has to agree, even if he's not allowed to say it publicly. He gives Raleigh an approving nod the next morning instead of a stern talk, and when Raleigh returns the nod, Stacker knows that he understands.