My work required me to learn how to make hard candy and it is indeed boiled and very carefully. Crystallization will ruin a batch. Stirring has to be done carefully and gently or the syrup will splash and a crystal will form and drop back into the mixture - supersaturated - and the whole thing goes cloudy. It is a hot, sticky, thankless job. Lollipops are boiled sweets - nice and clear if done properly. So are Life Savers and lemon drops.