We were speaking of skin contact with the 12V source, not anything else.
I work around multi-hundred amp power supplies all day, routinely strip off my watch and ring, and bump or lean against terminals for voltages from 3.3V to 48V. Still here. The danger labels we stick on refer to tool contact, not skin contact. My ring measures about 20 milliohms. At 12V, that 7200 watts. Simple resistance heating, very hot. But so is grabbing the wrong end of a 40W soldering iron. Neither have anything to do with resistance heating of the skin itself, caused by current passing through it from a low voltage source.
I think PZ said that using good handholds with saline reduced contact resistance to less than 5K. Lets assume I'm off by 80%, and go with 1K ohms. At 12V, that's 12mA, or 0.144 watts, 1/10th the power of a flashlight. One hour of continuous contact would be 0.144 watt-hours, or 0.000144 KWhr, or about 124 calories. In one hour, this would heat 1 cup of water about 1 degree F.
There is a long way between the milliohms of rings and the kilohms of the skin underneath them. The internal impedance of the body is very low, but any current must get through the skin first. It is a simple series circuit, where the current is limited by the highest resistance in the loop.
Of course a zapper is different because it isn't simple DC, but there still are several orders of magnitude between the max possible electron flow with a 12V source, and medium-rare.