I'm guessing that the system compares how bright it is in front of the car with the amount of light hitting the mirror.
If the front-facing sensor says it is dark in front of the car (i.e. nighttime) but the rear-facing mirror sensor says it is bright, then the computer calculates that it is driving at night and someone is behind you with headlights and dims the mirror.
Without the front sensor, how would the computer know if the light hitting the mirror was sunlight or a following car's headlights? It couldn't work out when to dim the mirror.
Just a guess and could be totally wrong.....