I would understand “he never left the ground and flipped over” differently. Just based on having seen the photo series of the incident.
I think it felt to her as if he “flipped over”, because his body pushed across but then he dropped out from under her, and she ended up on the ground. “Flipped over” could refer to the sloppy way the momentum propelled him over the obstacle, while leaving his legs on the other side.
Her use of expressions could easily be understood in different ways. She wasn’t speaking very precisely. I think that what she said probably did express the way it felt to her.
Had the horse not managed to get his front legs back under him, it could have been a true head-down feet-up cartwheel. Lucky that didn’t happen.