"Battery Charge Visit Workshop" Insight Needed

My girlfriend's mom's 2006 S350 had this warning message appear on her dash on the way home in red. I looked at the voltage via the cluster, and the car had 12.2V before being started and then held a constant 12.0V with the vehicle running.
Is this indicative of a faulty battery? Could it be the alternator? Car has 66,000 miles on the original battery.
Cheers,
Jeff







