To a large extent the same applies to mouthpieces (although density of material can have an effect on sound when the tip is less thick). There could be some subconscious reason people may think metal would be brighter because it looks brighter. Or perhaps this is one of those myths that stems from band directors' misconceptions. Imagine a band class of beginners, all of whom have the stock hard rubber beginner mouthpiece. One of them buys a metal mouthpiece that happens to be bright because it has a narrow chamber and high baffle and sticks out like a sore thumb. Band director (who knows very little about saxophones) blames the metal.
What makes a mouthpiece bright is very often the baffle or chamber size.