There should be a couple of clarifications that we need to establish in order to be sure that we are on the same sheet of music here. Aiguillettes are basically a badge of office for the wearer to distinguish them has holding a position of importance. Aides to general officers, admirals, secretaries of various military branches, the president and vice-president are all called upon to wear an aiguillette. These positions are only held by military officers. So, to answer your question, the regulation is correct regarding the wear of the aiguillette. I believe that the illustration that you are showing would have been correct for the service dress (Class A) uniform for either an officer or an enlisted soldier. Obviously, the regulations changed when the army did away with the green "Class A" jacket. Aiguillettes worn with the dress blue uniform are attached beneath the shoulder board.
Be sure to understand that an aiguillette is NOT a fourragere, which of course, is a unit award worn by soldiers of units who were decorated by foreign governments who bestowed such awards. Fourrageres are worn buttoned to the shoulder strap. When shoulder boards were worn with the dress blue uniform, a button was stitched to the proper location on the shoulder in order for the fourragere to be worn properly.
I hope this helps.