Yes, it is technically true that it is the current that disrupts the heart rhythm. Theoretically, a 9v battery can supply enough current to cause a potentially fatal heart arrhythmia, if it's shorted through a person's blood. But it's also being pedantic.

Consider Ohm's Law: `I = V/R`. Why is it so frequently printed in this way, rather than the simpler `IR = V`? If we don't care about simplicity, why not `V = I/R`? What is special about `I = V/R`?

Resistance--be it your work load or your human fleshy bits--is usually roughly considered a constant--or at least a known--for a given application. And most power sources that you'll encounter in the wild are voltage-controlled and able to supply practically as much current as you want (aka "more than enough to kill you"). So Voltage is the independent variable, leaving Current to be the dependent variable.

While it is true that "it's the current that gets ya", it's the voltage over which we have control, so we tend to focus on that instead.