Great advice. I've ridden two horses that really had a problem with this. I used a running martingale on one with great success. The other just naturally held her head high and even hit me in the face a few times because of it. Each horse is so different.
Follow this advice, I have a gaited mare who held her head high (and tight) too. This same advice was given to me by my wise instructor who, if she can, also avoids such contraptions. It worked for her, she now relaxs into the bit.