When current goes through the chest that is what can stop the heart.
One other point just because someone doesn't die immediately doesn't mean the are free and clear of consequences. Even if the electricity doesn't go through the chest the current could cause blood clots from the electricity essentially cooking your blood.
As a example before all the "job killing rules" from OSHA that the repub's gripe about now and want to do away with. The rules on lock out tag of of electrical equipment was lax to put it lightly. I was working on a piece of 3 phase 480 volt equipment. It was kind of tight because of the metal scaffolding that had been built and my shoulder was pressed up against the metal scaffold. Someone further up the line energized it while I was working on it. The current went through my hand to my shoulder. I was lucky in a way the route it took since it didn't go through my chest. But even though it didn't kill me. I still could have blood clots form from the power cooking the blood in my veins. Again luckily for me it wasn't that severe and I didn't have a problem afterward.