If they say doors may shut 40 seconds before departure I don't see how they can reasonably say "Oh well actually we shut them more than 2 minutes early but really you shouldn't have expected us to actually do something as difficult as waiting for the correct departure time and it's your fault for not getting there earlier".
I think common sense applies here.
You’re right that trains shouldn’t leave early, and where that happens something has gone wrong, but for long distance services it isn’t unreasonable to expect people to arrive in good time and board the train with a few minutes to spare. My operator states that train boarding closes two minutes before booked departure, and train details are removed from departure screens at that point.
In reality doors aren’t closed quite that early, but this is done to facilitate an on time departure, and to reduce the risk of PTI incidents. Sadly it’s still very common for people to arrive late for their train and then take it out on the dispatch staff when they’re unable to board.
I've lived somewhere that I commuted from a station a few minutes walk away. I knew how long it took to get there. I usually cut it fine, getting to the platform 1 or 2 minutes before the doors shut. If the train had left early (it never did) I don't see what that should be mine and not the railway's problem.
That approach is fine for commuter trains/the tube - I do the same myself - but not sensible for infrequent long distance services, especially those for which you hold an advanced ticket and therefore need to be on a specific train.
I use RTT a lot though admittedly I only use a small part of the rail network but it's very rare for me to see a train showing as departing early and I certainly haven't ever seen a station where trains are consistently shown as doing so.
I’m fairly obsessive about timings, frequently check RTT reports of trains I’ve worked for interest, and regularly see them shown as departing “-1” when I know we have departed with the second hand more or less on the hour at booked departure time. I certainly wouldn’t take a RTT report as gospel proof that a train has departed or arrived early.