Electric fence chargers use a pulse-mode power supply which charges up an inductor from the battery and discharges it into the fence. The inductor stores a specific and limited amount of energy each time it's charged. When that energy is discharged into the fence, the voltage, current and duration are determined by the impedance of the fence and whatever's in contact with it.
If the soil is damp and your hands are wet & salty, the energy will be dissipated quickly, with a lot (relatively) of current and little voltage rise. If it's dry, the voltage will rise higher, the current will be less and it will take longer. And if there's nothing touching the fence at all, the voltage will be quite high and stay there for a long (again, relatively) time while the inductor's energy is dissipated into the air.
Because the energy is limited, the voltage or current (bot not both) can be quite high without risk of electrocution.
It's not just the current that kills, it's the current and the duration. I2t ... perhaps you've seen that somewhere else?