I am of the view that the blame for the poor actions of some staff is down to management.I could go on, but it seems the verdict has already been reached. The Gatwick Express is bad and all the staff are liars, cheats and charlatans
And, to be fair, of the dozen or so people on this forum who I am aware have used Southern tickets on Gatwick Express operated by Southern, back when on-board inspections took place as a matter of routine, only a minority of them were charged.
But why not go for the Southern Only fares? The definition is in NRCoC Condition 10, it is restricted to the trains of a particular Company. The Company is Southern. There is no Gatwick Express Company currently operating trains, it is true that some Southern staff (including managers) pretend that there is, but when asked by the DfT they "agree that there is no separate Gatwick Express franchise or Train Operating Company" (source) the old company is still in the name of National Express.. I had no idea that price was available on GX and always go straight to the "Southern only" fares!
It is unlikely that you would be challenged on such a ticket, but if you are, simply take a copy of the Southern route map. "Other operator" services are shown in a thin black line. Gatwick Express route services are clearly shown in a thick red line as the "Gatwick Express route".
It's a brand name, the service is still operated by Southern. Their website admits this, "(c) Gatwick Express is operated by Southern". The NRT also correctly shows the operator is SN (Southern).
Greater Anglia only tickets are valid on Stansted Express, there's no difference in status. Both Stansted Express and Gatwick Express are brand names.