From a Neuroscience Point of View
Current is generally what kills but current and voltage are linked together via Ohms law so both can be a factor.
What the article was saying is, if you place a voltage across a nerve cell you can hyperpolarise it (meaning it wont fire at all) or depolarise it (meaning it will fire once then probably die because it can repolarise). This is how if you shocked the nervous system directly you could kill someone.
The current or voltage does not have to be applied across the heart to stop it. If you disrupt the pacer signal from the brain to the heart, the heart wont beat either.
As for the tongue thing, I heard that by placing a 9V battery on your tongue you can cause the nerves to contract around your mouth which can cause you to swallow it.