I can see it from both sides. I can clearly remember those couple generous souls who saw a kid/preteen girl that loved horses and offered to let me ride. I was so thankful and now I try to give back to kids whenever possible because I remember that feeling of pure JOY of just being on the horse. It was awesome.
Now that doesn't mean that every horse is a good match for a kid. One of the ones I was on wasn't. So you have to exercise your best judgement when it comes to the safety of the horse and the kid. I do think the "not allowed to touch" comment was over the top and rude. And tbh, it probably would have broken my 12 year old heart to know that I wasn't allowed to pet a horse. I hope you didn't make that comment directly to the kid.