The battery light is really misnamed as it normally tells of a problem with the alternator.
I've never heard of an alternator or battery that sets a code when it fails but things change so who knows.
If your voltage really was at 8.1v then you were not charging. At rest a car battery should have 12.6 volts at least and when the car is running it should be higher than that, normally I would say between 13.5 & 14.5 volts.
If the battery is boiling over that would indicate an overcharging in the system.
How is the voltage regulated in this system? Is the regulator internal to the alternator or does it regulate through the computer?
If this is an intermittent problem the testing that was done at the rebuilders may not be conclusive.