At the Montreal Olympics Princess Anne fell off at a vertical made out of fairly narrow round wood pieces on undulating ground. Then was helped to remount and continued even though she had a concussion and afterwards didn’t remember the round.
She did not also fall off at the water - just the one fall in that round. She went on to complete the SJ the following day, even though the British Team did not complete.
What annoyed me about the episode that was supposedly Badminton: first that they called it a “show jumping career” but then were otherwise accurately portraying that it was 3-day eventing. Second (and worse) they called the horse, a chestnut, Goodwill (who was black)! At the least they could have fudged it by not mentioning a name at all!
I read an article that described the stand-in rider, she is a young rider doing very well in show jumping. Obviously they had to go with whatever horse she was riding.