That's not necessarily true by the way. Carrier oils become rancid and smell horrible after awhile. Essential oils will either get stronger (the same smell, just more dense), or weaker. Patchouli, rose, and jasmine all get stronger with age, and are considered better - like a fine aged wine. Citrus oils all become less effective and weaker with age, flatter and with less dimension.
Synthetics are a whole nother story. Some will smell worse with age, some better, and some (like my mom's Shalimar) won't really change much, if it all.