There is no information displayed to passengers that pressing the alarm button will require the train to stop, the driver to walk back through the train to reset, and then walk back through the train again to continue. In these circumstances it's not unreasonable in the slightest for passengers to think the alarm button is just a way to contact on-train staff in an emergency situation so that they can tan take the appropriate action in the circumstances - which would certainly include calling ahead to arrange an ambulance to meet the train at the next appropriate location.
Passengers cannot be expected to know which services have guards and which do not (and if they do whether they are in the same portion of the train as they are) or what the next suitable location for an ambulance to meet the train is (while it's not unreasonable to expect passengers to know what the train's next scheduled calling point is, it is not reasonable for them to know where they are in relation to any intermediate stations, whether any of them are suitable for an ambulance meeting a train, and if they are whether the train was scheduled to pass through on a line adjacent to a platform).
Really there needs to be two options:
1. There is an emergency situation that means this train (almost certainly) needs to stop before the next scheduled calling point.
2. There is an emergency situation that on-train staff need to know about but which does not require the train to be stopped right now.
Yes indeed, that's the point I was trying to get at. Doubtless it would be abused/used incorrectly as things always are, but given that there are some people left in the world who think about their actions, clearly presenting these two options doesn't seem too hard and even if used only sometimes would improve matters. I think there is scope for some passenger education - again it won't sink in to everyone but some will listen. We are bombarded with announcements, some useful, others less so - I think there's room to fit in something in this area.