Not sure what you mean? My point was First Greater Western, operating under the brand GWR, operate all trains from London to Didcot, however under the guise of Off-Peak restrictions limit travel on cheaper tickets to their less premium, slower trains, rather than their 'express' IETs.
If GTR is told it can't sell 'Southern ONLY' tickets, surely GTR, operating under the brand Southern, could introduce trains which run express Brighton -> Gatwick -> Victoria, again still using Southern branding but perhaps with a nicer look, nicer seats etc, then use ticket restrictions to restrict cheaper ticket types to only travel on slower services. If GWR are allowed to do it, Southern can too, and it is a brand restriction by proxy.