Final answer:
The claim that the Americans won the Battle of Bunker Hill is false; the British technically won despite suffering heavy casualties, which elevated American morale and led to British leadership questions.
Step-by-step explanation:
The statement that the American forces achieved a victory at the Battle of Bunker Hill due to the actions of British General Howe disobeying military orders is false. The battle, technically won by the British since they were able to drive the Americans out of Charlestown, was actually a pyrrhic victory due to the very high casualty rate suffered by the British forces. General Howe, who later took command from General Gage, was responsible for the heavy losses by ordering frontal assaults against fortified positions. The battle showed the resilience of the American forces and boosted their confidence while devastating British morale and leading to questions over British military leadership.