I have been with multiple barns (each teaching a different stage of riding: one the basics, the second how to be safe and confident at around 1m, and the third going up into higher classes) and not one allowed jumping without a trainer in a lesson for safety and some liability issues.
As in the trainer's horses or the client's horse? If the latter, then I can't see why they would stop them. The client has to jump on their own at some stage and develop their own sense of awareness. I wouldn't think they're a good trainer if they have to micromanage everything, unless the rider is novice.
If it's the former, I can see why they'd be hesitant but again, the client will have to learn to develop their own sense of awareness at some stage too.