Thats not quite accurate- it is true that high amp current is deadly in many scenarios, but it takes both amps and volts to kill. High amp, high voltage current is a killer for sure, but high current at sufficiently tiny voltages is not necessarily deadly. Similarly, high voltage at low currents is usually not deadly (but can be very painful).

You need to be introduced to a classic: https://www.youtube.com/watch?v=XDf2nhfxVzg

Your comment is completely irrelevant to wall sockets because they can all supply more than a tenth of an amp.

High voltage from a Tesla coil not only has low average current, but is subject to the skin effect. So while it can still cause a painful shock to your superficial sensory nerves, not much of that energy ends up in contact with the motor nerves.

TL,DR: you probably don't want to be shocked by a big Tesla coil, even though it won't kill you.