Mirror Universe Riker is actually the non-bearded one. Starting in Encounter At Farpoint, the non-Bearded Riker has already ambushed the Bearded counterpart from the Prime Dimension, and has snuck aboard the ship to cause problems.
The problem is diagnosed and solved by the advent of the second season, which brings with it the return of our own lovable Will Riker. The reason this was not caught on camera or mentioned in any way, is because the entire affair was simply too boring to be logged.
