I read once that a 'load' gets only the current it needs from the battery / voltage supply.. So, why the LED gets more than it needs and dies when connected directly to the battery?
This is a very vague statement. If the load is a resistor it draws the current defined by Ohm's Law.
If it is a led , without a current limiting resistor, there is nothing to limit the current so it will draw as much current as the source can supply until it melts (or vaporizes) the junction.