I think it’s fair for blood elsewhere than the mouth to only be elimination at the discretion of the GJ, because a small amount of blood from brush, or even stumbling and interfering is not only essentially harmless but can clearly be seen to have not been caused by the rider.
Blood in the mouth is a bit different, because although it’s certainly possible that a horse can bite its lip or tongue due to a stumble it’s tougher to be 100% confident that the rider and/or bitting setup didn’t contribute to the issue, even if the actual injury is extremely minor.
I’d be in favor of blood in the mouth being an automatic elimination, and leaving blood elsewhere to be eliminated at the GJ’s discretion.