05 Ford Five Hundred charging system message?

05 Ford Five Hundred recently over night problems with the charging systems came up. The has a new (rebuilt) alternator and starter that were put in within the last 4 months. Battery is 18 months old (Motorcraft). All of the sudden on Monday freaking morning the dashboard has a message on it 'Check charging system', then the battery light comes on too. Here is the catch the car turns on and drives.

Took it to the repair shop that did the alternator. The man hooked up the tester to the battery to check the system. According to the tester everything is running fine. They will look into further this week. But what in the world would cause the message to come up and yet the car runs?

The car will run until the battery goes dead and leaves you stranded. The rebuilt alternator is probably bad.

The battery light doesn't indicate the condition of the battery, it's whether or not it's being charged.

Everything I have read is pointing towards changing out the rebuilt one for another one. I did read another post that a New one would be better. (PCU) commands the voltage regulator in the alternator to deliver the voltage it wants by way of an electronic signal on a line to the alternator. The PCU then verifies that the message was received by looking for the same signal to come back from the alternator on a separate line. In our case the voltage regulator was not sending back the confirmation signal and the PCU lit the light because it suddenly didn't know what the alternator was doing is my guess.