Wembley Central has very narrow platforms and is somewhat of a wind tunnel. Thus, access is not available to the fast line platforms at all, and on the slow line platforms access is only opened after no train is going to pass through before the arrival of the hourly Southern, and closed once the platform has cleared post departure. It's a unique way of operating that I'm fairly sure has signage of some sort, and seem to recall it's only enforced by way of Tensabarriers. For that reason, if you're wanting to photograph a train on the WCML Wembley Central isn't the place to do it, as access is almost certain to be refused for anything other than the purpose of boarding/alighting from the Southern.
Only the Overground platforms are accessible at all times.
From what the guy was saying it sounds a bit like the YouTuber may have ducked under/opened that Tensabarrier himself to get onto the platform. If so, while I don't think anger is a sensible response to any situation, the member of staff would probably have been within his rights to chuck him out of the station for entering a non-public area, which is actually a Byelaw offence for which he could have technically been prosecuted - but ideally to do so politely - "I"m afraid I'm going to have to ask you to leave the station because..."
It's a very unusual case indeed, the only other place this sort of thing is in place (that I know of) is Bushey on the down fast, though I suspect you'd also get short shrift if you were the wrong side of the fast line gates at any other south WCML platform, if only to avoid the risk of suicides. That is different of course because it's easy enough to film from the correct side of them just like a lineside fence - at Wembley Central there's no permissible place to be where you could clearly film trains on the slows or fasts aside from the arrival/departure of the Southern service.