Morality requires God

Overview
It is often claimed by theists that morality requires God, i.e. people only behave morally because of belief in the carrot-and-stick of reward/punishment from God (Heaven/Hell).

This claim is a special case of the claim that morality requires religion.

Conclusion
The clinical term for people who behave decently only on threat of pain and/or promise of reward is "psychopathy". This claim is therefore equivalent to a claim that humanity is generally psychopathic. Studies show, however, that psychopaths actually make up only about 5% of the general population.

This claim is therefore absurd if applied to humanity as a whole or to the overwhelming majority of individual humans.

It may, however, be applicable to the majority of religious leaders, as psychopaths account for a disproportionate percentage of people in positions of power.

Implications
If moral behavior requires knowledge of punishment and reward from a being more powerful than humanity, this implies a few things:
 * Humans did not behave morally before discovering/inventing this particular form of God (e.g. ancient Romans, ancient Egyptians, Mesopotamians).
 * How, then, did civilization arise, if nobody could be bothered to treat other people decently?
 * Entities who have not received instruction in this aspect of religion do not (or cannot) behave morally.
 * So... Hindus, Buddhists, and Confucianists do not behave morally?
 * Adherents of any monotheistic-disciplinarian religion, such as Islam, will unfailingly behave more morally than those who are not followers of such a religion (atheists, Hindus, Buddhists, Confucianists, etc.)?
 * Non-human animals cannot behave morally, since they cannot receive religious instruction.
 * There has recently been some evidence against this...