Why don't electric fish shock themselves?
physics.stackexchange.com
physics.stackexchange.com
Of course, the insulating fat also likely provides a sort of faraday cage effect - any current that does hit the eel will just flow through its skin instead of hitting anything important.
Having just done a very very quick search of relevant papers, I'm not entirely sure that anyone has actually looked into this. So the scientific answer would best be "I dunno".
However, you might contend that the electric current in an action potential moves across the membrane, not along it, and you would be correct. But that is because the voltages involved in the action potential are oriented across the membrane. The electrical conductors that carry this current are aqueous solutions of sodium, potassium, chloride, and other ions, and this solution will happily carry a current in any direction in which a voltage is applied. So when an external source (like an electric eel) supplies this voltage, the muscular tissue conducts the current. The ion channels in the membrane also ensure that the current is not stopped by the membrane as well.
Fat has high electrical resistance because lipids are predominantly hydrophobic and nonpolar, which means that they exclude both water and ions, both of which are necessary to carry a current in living systems. Muscle has a low resistance because part of its function is to carry an electric current.
Incidentally, if you think muscle doesn't conduct electricity, you might want to consider why the eel would even bother with all this electricity anyway. What's the point of zapping your prey if it doesn't even conduct electricity?
Moreover: cut the conductor and the muscle doesn't move. Which is why nerve damage is so crippling. You literally have lost the ability to signal the muscle.
According to the second answer the Eel is more resistant because it has a layer a fat. Unfortunately, there is no evidence of that, but at least it makes sens.
I thought you meant....
"it was extremely painful for me to watch [myself from outside my own body]."
What disturbed me most was the prolonged length of the event.
Science continues to show us complexity that defies chance explanations, and speaks eloquently of the Creator's hand.