Which is the Sensor are you referring to? Where is that located?Maybe whatever the sensor that is used to "check" the alternator is bad and throwing the light? If you have code reader maybe you can dynamically read what voltage the sensor is sending to see whether the sensor is bad which may cause the light to turn on? for what it is worth, when my alternator was dying, the "battery" light never came on.
it reads between 12.2v and 12.6v when the engine is not running.What does your battery measure under load? What is the voltage drop when you are cranking the starter?
When the engine is running, I was able to see the it reads between 13.6 and 14.0v all the time ( 13.6v with all the power drains like heaters, fan, viper etc).