Train Stations are not public spaces. They are private property, which you are permitted to use based on particular criteria. Holding a valid ticket is the main one, obviously. Yet a valid ticket doesn't mean you can go wherever you please within the premises, certainly not onto a platform that has been designated for private use, and not expect to be moved on.
The operators do not own the station, but they are granted authority over platforms where their arrivals and departures occur. Bigger operators tend to use the same platforms all the time, so in a lot of cases, Virgin platforms are always the same. Their platforms are their remit during the time that an arrival or departure is due. If they decide a part of the platform is for private use, they can do so, as per being given the remit of the use of private property.
Also, you need to have the permission of Network Rail to film anything in a train station, so, private platform or not, he's still in the wrong (unless he was granted that permission, which I am going to assume he wasn't). And he's sticking the camera in the faces of people who clearly don't want it there, as clearly demonstrated by Fellaini's reaction. When he is spoken to reasonably, he erupts and acts unruly and uses profanity. He is the one breaching the peace first and foremost. He's no way in the right, for a number of reasons.