Thanks, Bay. I know battery chemistry and charging systems in general very well. I just don't know which logic Nissan used in 2009.
The old "classical" rules for charging haven't been universal, or best, for a decade now. A full battery in theory, ignoring the alloy blends used, would be 2.2 volts per cell times six cells, or 13.2 volts. In practice the alloys used (except for TPPL pure lead cells) tend to be 12.6-12.8 volts when charged, with Optima claiming 13.2 for some of their lead-tin alloys.
This is just a generic battery and as I said, it is the second one in the car, not the original. Screwing around with wet acid and hydrometers certainly works, if your clothes are worthless. These days, a voltmeter and knowing how to use it can tell you just as much if not more, even if it doesn't allow for cell testing.
The best modern chargers will "lead" battery voltage by a fixed amount, and put all the rest of their power into increased amperage. This provides more efficient charging, because there is less boiling (microbubbles) in the electrolyte. I don't think the Murano has that technology, and I don't think it would reduce to 13.2 volts for a 12.2 volt battery out of intentional intelligence. I think the charge controller, which may be part of the ECU rather than a traditional integral alternator/regulator, may be at fault.
But there are so many variations on the market these days, it is impossible to make any reasonable guess at fixing things unless one knows what the factory system's normal behavior is.
For instance, most chargers and alternators in the past 15-20 years will not put out ANY charge if the battery drops below 10.5~11 volts. This is to prevent some dummy from trying to charge a really dead battery, resulting in some of the 10,000+ battery charging explosions in the US every year. But hook up a second power source to "show" 12 volts? And the dead battery can be charged with no problem. Usually.
The old 2, 3, or four stage dumb chargers? Treasure them. The new ones are way too clever for many purposes, good at others like not overcharging. Sometimes.