Just to add something not at all important on this.
As you move away from the source of the voltage in water, the conductance goes up with the cube of distance because the half sphere water volume away from the source is expanding and hence charge carriers increase with the cube of distance. At some distance away from the source, the conductance is so high that for all purposes, its zero ohms to earth ground so basically ground.
In salt water, the conductance is already about 1000X higher than clean fresh water. So in salt water, the voltage goes to zero very quickly because the conductance increases so fast with distance. Or in other words, the resistance goes to zero very quickly. Where resistance is zero, there is zero voltage drop.
But in fresh water with much lower conductance, the voltage can extend out a much larger distance before its effectively zero. You dont need to be touching any ground, the danger is having your body where there is a voltage gradient or field.
That distance might be a bunch of feet in freshwater so a swimmer can get close enough to the source where there is still a voltage potential over distance (ie, voltage gradient or field). Its the AC voltage potential difference across your body that kills. The current might be very low, not enough to cook anything.
Remember that the conductance increases with the cube of distance away from the source so it also means that a swimmer might feel nothing and the within a short distance, encounter a field (potential across the body) that messes with the heart.
In salt water, the distance are so small that the swimmer would almost need to be touching the hot electrode.