Yes its true.
Its possible that your heavier arrow will shoot FLATTER out at 30 yards than a lighter one going abit more speed. It has to do with the coefficiency of your arrow weight/speed.
Supper light arrows going blistering fast will not hold the kenetic energy long because they tend to slow down faster than a heavier arrow going abit slower. They dump their energy quicker than a heavier arrow. Food for thought.