Too many hot peppers consumed in a short amount of time can indeed kill you but you would have to eat thousands of the hot peppers in one day before the hot peppers actually did kill you.
You'd likely give up eating the hot peppers before you even reached 100 hot peppers so while you'll likely have a burning mouth and a burning stomach and hurting stomach you'll likely never be able to eat enough hot peppers that would kill you.
Some people have become really sick though when doing a Hot Pepper contest but most people do survive eating all those hot peppers but you are unlikely to die as a result of eating too many hot peppers because your body would not allow you to eat enough hot peppers for it to kill you.
Still eating too many hot peppers can cause ulcers and other stomach problems so it's not recommended to eat too many hot peppers.
But in moderation hot peppers are very healthy for you and can ward off diseases and boost your bodies immune system.