Final answer:
The claim that Britain responded to colonial opposition by increasing stamp fees in the Declaratory Act is false. The Act asserted Parliament's authority but did not impose new fees.
Step-by-step explanation:
The statement “The British response to the colonists' reaction was to 'double-down' and impose stiffer stamp fees in the Declaratory Act.” is false. Instead, the British government responded to the colonial outcry against the Stamp Act by repealing it in 1766.
However, at the same time, the British Parliament passed the Declaratory Act, affirming that Parliament had the absolute power to legislate for the colonies “in all cases whatsoever,” including the power to impose taxes. The Declaratory Act did not impose stiffer stamp fees; rather, it served to assert Parliamentary authority after the repeal of the Stamp Act, setting the stage for further conflict between the colonies and Great Britain.