Only so far as voltage is required as the
potential which causes current flow. Current flow is a function of voltage and resistance, and it cannot exceed the capacity of the source. It is
current flow which causes work, not voltage potential.
The low end of 30 volts is based on the lowest body resistance of the human body.
Actual current flow, and length of time exposed to it, is what causes damage. Current flow is the flow of electrons, and flowing electrons causes physical damage to human tissue through heat damage, as well as electrical interference with the nerve signals which control the body (namely the heart). Voltage potential is just that...a potential: it's not a measure of electrons flowing through anything. You can have high voltage potential with zero current flow.
It takes 30 mA of current minimum across the heart to cause ventricular fibrilation. How that current is acheived is a function of body resistance and applied voltage. Changing body resistance means changing the required minimum voltage to induce that 30 mA of current flow.
There are other factors which influences the severity of electric shock. You can take quite a bit of current above 30 mA without cardiac arrest, for example, if the current path for the electricity does not take it through the heart. You may have serious burns on othe parts of the body, but the heart will keep right on trucking.
Frequency makes a difference, as well. DC is worse than household 60 Hz. High frequency electric shocks can produce a "skin effect", where the current flow is across the surface of the skin or through the skin layers, without penetrating deeper, which means very little current flow actually passes through the heart even if the shock is across the chest.
But the medium by which damage occurs is ALWAYS current. Voltage is just the potential which causes current to flow.
Otherwise people would be dropping dead right and left in the dry, winter months when they build up enogh static potential walking across carpeting snd such to reach upwards of 20,000 to 25,000 volts.
Trust me...electrical safety is an integral part of my job and has been for decades now.