That sounds like a good description of an ETI trail trial. Odd, I never thought much about the rules. I just decided I wanted to compete so went along with whatever they required. I guess that's how I look at any competition, what do they require and can I do it?
I consider competitive trail a step up from trail trials, it requires more training from the horse and a better rider. I call trail trials the old lady sport, it's pretty safe. :)