"Battery" light is actually more correctly identified as a "Charging system indicator" light. Has NOTHING to do with the battery. You could, technically (though unsafe), remove the battery from a running car and the light wouldn't come on. (though would be VERY deadly if you moved a hot load wire from the alternator to a ground or yourself!)
The light is indicating a potentially failing alternator, or the wiring between the alternator and the Battery POSITIVE, or the alternator and chassis ground.
Ray
