They are not contradictory. If you set up for a Cat IIIB (dual) approach and you get a downgrade to cat III single then you go around. If you can't then fix what caused the downgrade then you can fly a cat IIIA (single) approach, providing you have the required minima etc.
There's absolutely nothing wrong with flying a cat III single approach on one autopilot (e.g. If the other was Inop at dispatch or had failed inflight prior to your FAF/1000')