I really don't understand all the scientific issues, but I know one thing: people already are using enough medication on competition horses that does not follow the rules. While the USEF rules are more relaxed than the FEI rules on medication in s...
the cross rein method would probably be when you're using split reins and the would cross over the withers. A rein would be attached to the bit, run along side the neck and the come over the withers.