Bear in mind that I was just trying to figure out why someone would think this and I was NOT stating I believed it.
If a rider is leaning on the reins, all their pressure is directly on the horse's mouth. If the reins are passing through the bit and to the girth, wouldn't some of that pressure on the mouth be lessened and distributed to the girth as well?
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Good thought but no, the rings of the martingale make the rein a lever with it's fulcrum being the ring of the martingale. The applied force of the rider's hand is multiplied by the ring to make a greater the product force- which is the force on the bit.
The strap on the girth is just an anchor so the martingale stays somewhat in place.