Maybe the inspector felt his presence was causing more anxiety, and that the best thing to do was to remove himself from the situation in the hope that it would help the OP to calm down? Unless he left her on her own I'm not sure this is irresponsible.
Two other officers took over from him and offered help. These people must have been near by. It may have been better for them to take over as they weren't involved in the original situation and could therefore sympathise with the OP and suggest she appeal the ticket to try to calm her down. I suspect they ended up calling an ambulance so they could have the passenger removed from the tram (make it someone else's problem) and avoid any liability if anything were to happen.
My only other comment is about the inspector being "nasty" - why would he do this? The OP needs to remember that it's his job to deal with passengers without tickets, it will be a run of the mill situation to him, the lack of a ticket won't have hurt him personally so there would be no need to be "nasty".
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Reasons. I can only speculate.
A one or two day course can never cover everything.
Compensation Culture. I can imagine the lawyers having a field day. Poorly trained railway first aider made it worse.
This is interesting because when I've done first aid courses, they've always said that provided you follow the training and don't do anything completely stupid, you are unlikely to be successfully sued. I am not sure if there are any documented cases of people being sued for first aid attempts but I do think this is probably another myth.
Having said that, the one time I've seen a passenger taken ill on the train, it was a DOO only service. So it was left to me as a fellow passenger to assist while two of the other passengers argued about whether or not to use the alarm to alert the driver on the basis it might delay the train...