My opinion for what its worth. As long as your horse will listen to you when under preasure what's the problem. Even a horse that is controlled with a bit will take it by the teeth and bolt if in fear, and the bit won't stop it.
A calm head by the rider can bring it back under control. Having a horse that will give you its head when asked will respond to a one rein stop better than one being hauled on by both reins while heading in a straight line.
Sounds like the person who made the comment about having to have a bit perhaps should try it for themself and decide which method is best. Hauling back on a bit and risk the horse going over backwards or turning the horse into a decreasing circle.
If you trust your horse to listen to you and it has good brakes and manners, then indicate to those who disagree to take a running jump.
I use a bit, however Stella has taught me she objects to me being to hard, by shaking her head, flicking her tail hard, and will stretch out her head, taking the pressure out of my grip and the moment I release she settles. She prefers a loose rein. But I learnt that from the horse, by listening to her.