I do not understand a couple of things. Ok, I don't dive a treb, but a Sidekick. I have the oxygen 3 liter on the ccr on my left side. I can open and close it myself. Yes, I had 1 time the oxygen closed when swimming and walking with it at surface. But you see this when you check everything before you start the dive. Same when you forget to open it. Normally I open the valve, do calibrating and close the flow stop on the oxygen side and close the valve (I have a flow stop on the oxygen side as this works faster than closing a valve when needed and before a dive you don't loose oxygen due the leaky valve/orifice). When everything is ready in the water, I open the valve, check the mav and the flowstop, and check PO2 on handset. Even if you start your dive with a PO2 of let's say 0.4, you bring it up with the mav as a check that everything works.
So why won't you see that the oxygenvalve is closed in the first minute of a dive? Check every minute the handset is also not done then.
Entering the water with both ox and dil closed will mean that you cannot dive. When you jump in with everything closed, that is possible when you did not do your checks, but as soon as you go down, the ADV will not work and even the MAV not. So you cannot get gas in the counterlung. Starting a dive will not possible, only with a negative entry, but then you will have done checks at surface.
I think the Treb does not have a hud, but a hud helps for sure to detect PO2 problems. I also don't have a HUD on the Sidekick. But I have it on my inspiration.
Then another thing I do not understand. If you have an accident during a course with a student, you need to fill in forms and the instructor will be 'out', non-active, till there is found the instructor did nothing wrong. So if you made as instructor a big big mistake not to check the oxygen flow of a student and a deadly accident, you will normally already be 'out', expelled, but to make this mistake 3 times sounds strange.
Thinking about what can be learned I come to the routine and checklist.
A big difference I have seen between divers in Florida and in Europe is that ccr divers in Europe most times don't use a checklist. Yes of course they are there, also in Europe. But I have seen divers really use a checklist on paper in Florida and don't see it here. In the inspiration is a checklist in the handset, so you have to confirm you did everything. Revo also has a checklist on a card that you can use when you prepare your unit. I have seen using it in Sardinia. I think such lists will help not to forget things as open valves. But even then, if you have your own procedure and someone interrupt it, you need to check extra. If I dive my ccr, I tell students I need a couple of minutes for myself. Even if I teach. I help them with the unit and then I do my own. Same I saw in Sardinia last summer, the owner of the divecenter was on the same table where we made the diveplan for a 70m dive on oc. My students looked and looked why that diver was only busy with his ccr and did not react. I told them to wait, he need to concentrate on the unit. If you do other things than your routine, failures or mistakes are done. Experienced or not. In the Inspiration there is a risk that a diver thinks: again that list and confirm everything. And during the dive, ****, forgotten. I have seen that, so a checklist is also not that nothing will forgotten anymore, but at least you have confirmed that you did it.