All this time and I clearly misunderstood this addon - I thought if the simulator was pulling traffic with, say, the identifier prefix "BAW", Simple Traffic would always repaint it with a British Airways livery. I didn't think there would ever be a scenario where this would be "incorrect due to limitations" because Simple Traffic is just repainting based on the data the sim provides; in this case unmistakenly a British Airways callsign.
In short - Unless an airline livery is not provided by Simple Traffic, it should pretty much always be correct. I mean, How can the sim be providing the wrong data if the callsign of the aircraft is displaying, at all? If Simple Traffic is really "Simple", there shouldn't be much margin for error when matching callsigns.
Anyway - It's quite clear it's not working this way, on XBOX at least. It's a shame that this is how the addon is expected to behave (as confirmed by Devs in this thread) and I will wait for another solution.