Horse show circles aren’t usually very big - growing up I absolutely knew who belonged to which barn. If the student has shown with OP before and then went to the show and was a hot mess, it would make OP look bad to people who didn’t know the full story and that the student was there alone and without the trainer’s “blessing”.
I have definitely gone to shows to watch and see how different trainers’ students ride, how the coach coaches, etc. I pay attention to which coaches are encouraging, which ones yell, how they react when things go right and wrong, and seeing the same trainers year after year, I’ll be looking to see if their students improve or stagnate. If I saw a kid alone at a show being a general train wreck and saw that her trainer was doing nothing about it, it would raise some red flags for me because of the assumed association.
There are lots of complaints that h/j trainers are too “hand-holdy” - and in some ways I agree - but if I was a trainer and a horse show was my “marketing”, I’d be doing everything possible to make sure that my barn had a great time, stayed safe and did well.
Frankly, it seems that this girl’s parents don’t care if she’s ready to show or not and aren’t listening to OP when she tells them as much.