In my opinion, it shows your youth and relative ignorance to have such a black and white view of the situation. There are so many factors that go into actions and following actions that “hospital or get back on” is just to hard a line. My trainer and I have aged together, as she is a few years younger than myself but has had a different path in her youth that gave her more knowledge than me about certain things, which is why she is my trainer.
Her line has definitely moved over the years and while she generally advocated getting back on after a fall, it was never “must go back to doing what you did” There is generally a psychological impact as to whether or not you get back on immediately, in that often not getting back on feeds the part of the brain that wants you to avoid dangerous things - in other words, the last thing you did with the horse was “dangerous” (you fell, could have hurt yourself) and that thought tends to sit and ferment into a bigger fear.
That being said, getting back on is not always the best idea and getting back on and doing what you were doing before is also not the best idea. So, even over a decade ago my trainer would assess after a fall.
Let’s use an example of someone jumpin 3’ and falls off going over a jump:
scenario 1- both horse and rider seem fine physically and mentally, get back on, do the jump/course again. Assess what happened that rider departed from horse so it does not happen again.
scenario 2 - both horse and rider physicially fine, rider visibly shaken - get back on, walk around, relax, if that’s ok, trot, if that’s ok, canter, if that’s ok, crossrail, etc. Basically get back into things more slowly.
scenario 3 - both horse and rider physically fine, horse seems shaken - down to crossrails, move up, figure out what caused the horse to feel overfaced.
scenario 4/5 - either one looks injured, assess before moving forward.
She preached “grit” but not at the expense of physical or psychological damage.
More recently (both these incidents were last fall)
1 - I’m riding a new horse, we lunge him a few days and he seems fine, so she comes in, but of a lunge, seems fine. I get on and I’m having a bit of trouble steering and the like and we discuss that he (former racehorse) may not have learned that (some do, some don’t - but that’s another subject). Next thing you know he starts rearing, bucking and generally just throwing himself around. Technically, I didn’t fall off but she told me to dismount seconds after the behavior starts. She mentions she had seen him do this with the farrier also - he just seemed to feel like he was done and threw a fit. So remaining on (or getting back on if he succeeded in tossing me) would not have resolved the behavior. Instead, we lunged him until he was sweaty and tired and reassessed the training.
2 - a horse I had been riding a good deal, which is generally a sweet horse but BIG moving, LAUNCHED me in the air when he spooked at one of the employees mowing next to the indoor - the mower kind of suddenly appeared in view in a side door and he jumped, I got offsides and he jumped again at that because that’s not something he’s used to and the bolted because obviously I became possessed by a demon if I’m doing all this weird stuff. Both of us were physicaly fine but I was a bit shaken so I got back on and walked, trotted the next day and the day after I cantered again. Had I tried to canter that first day, I would have gotten tense, grabbed the reins and otherwise made a mess of the ride.
I posted similar thoughts in a thread in Hunter or Eventing on training a young horse - but the bottom line is everyone’s physical and psychological tolerance is different based on many factors so to judge someone for what they do after a fall is to show a lack of empathy towards different situations.