Voltage cannot be present without current flow, so if the correct voltage is present, then the alternator is supplying current to recharge the battery. HOWEVER, two observations:
1. It IS possible for a component in the charging system to be bad and to discharge the battery with the ignition turned off. It would be wise to check the battery's current flow with the ignition turned off. I would expect to see less than 100 milliAmps, and if there was more, I would start disconnecting circuits until I found the one that's loading the battery down.
2. When you use a voltmeter to measure DC voltage, it tells you little to nothing about any alternating current present in a circuit. If a regulating diode is bad, it is possible for there to be an alternating current present in the charging system, but if this was the case, I would not expect the DC measurement to be "on the money".
So, everyone has made a valid point regarding this problem.
