Final answer:
The not supported statement is that the British soldiers intended to unprovokedly shoot the colonists, as historical accounts, including Preston's testimony, indicate the soldiers felt threatened and did not fire upon the colonists with premeditation.
Step-by-step explanation:
The statement that is NOT supported by Preston's account of the Boston Massacre is that the British soldiers intended to shoot the colonists even though they were not provoked. According to historical accounts, the British soldiers felt threatened by the colonists who were attacking them with clubs and snowballs. Captain Thomas Preston, who was the officer on the scene, claimed that he never gave the order to fire, suggesting that the soldiers' actions were not premeditated but instead a reaction to the perceived danger. Moreover, John Adams defended the soldiers in court, indicating that there was some belief in their right to legal representation and the complexity of the events leading to the unfortunate outcome.