Good for OP for knowing that we, as horse owners, can tell trainers “No” in the interest of the horse. I respect trainers and their amazing knowledge, but ultimately, I’m choosing to pay them for services, and I’m the customer. I no longer work with trainers that don’t accept my views on nosebands, or other matters of horse welfare. I’ve literally said to trainers in response to advice to tighten the noseband that I like to allow them to tell me if my hands/riding are good or bad. If my horse is fussy, let’s work on fixing my riding (barring medical issue like teeth), not masking it with a tight noseband!
I have found with trainers that telling them I want to learn how to train my horse to be better, not win ribbons, helps us work together better. I’ve not had a falling out with any trainer over my views/desires - they may secretly think I’m a wimp/bleeding heart for my horses, but we still have productive lessons.