That's a mis-statement. First: go read up on
Black's Equation . Voltage isn't even a component: it's current density and heat. Yes, voltage can induce current but high enough current even with low voltage, at a high thermal state, induces electromigration just the same. By the same token, if thermal state is low enough even a high voltage wouldn't be harmful. Voltage in that case would be limited by the stress tolerance of the silicon, the point at which it can punch through die-electrics.
I also think you've not completely followed what BZ was getting on about in that linked video, and the one
following it. As an overclocker, your primary concern should be to keep temperature in control and keeping voltage as low as you can (at a given frequency, without instability) is the way to achieve it. You can't really control current, it's the inevitable consequence of the process and the silicon quality.