Helium does not kill brain cells. But a lack of oxygen does, and the practice of breathing helium instead of air (for the funny voice effect) can lower the oxygen content of the blood (and brain) to dangerous, even life-threatening levels without so much as a little discomfort.
I expect that's where the "Helium kills brain cells" myth comes from.
It's also why helium is the gas of choice for the "hemlock society."
In diving, helium is used to replace nitrogen (in very deep diving the oxygen level in the breathing gas is lowered too, but only to keep the oxygen level from getting too high.) and the oxygen content in the gas is kept at a safe level.
Rick