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I am first aid trained. It takes a day to learn some basics but is very worthwhile. Many workplaces will fund it.
Having a bit of basic training is really useful, every time I have had to assist the training just takes over. I have helped out at roadside incidents, neighbours having trouble etc etc. On a few occasions I have just found people milling around a casualty but uncertain what to do. Having a plan of securing the area (getting someone to direct traffic or hail down a bus to shield the casualty), getting someone to call emergency services while you get on with assessment and can then instruct emergency services is a huge assistance. When the response team arrives you can brief them and hand over, stay if they need any additional help and then go about your day.
Sometimes the best thing to do is leave it to those more capable to help and give them the space they need to work. If it's something that plays on your mind after maybe seek emergency/first aid training so if a time comes along when you are the first one there then you are prepared in some way to help, often tho I think little can be done by lay people in these circumstances.
My thoughts are with the rider, do hope it's not as bad as the few tweets I've seen sound.