Final answer:
The statement is false. Under Dillon's Rule, state power and actions are held above local governments, meaning the state government will typically have supremacy in the event of a conflict.
Step-by-step explanation:
The statement, "According to Dillon's Rule, if a clash were to ensue between a local government and the state government, the local government will always win," is False. Dillon's Rule is a legal principle that holds state power and actions above those of local governments, declaring state governments to be sovereign relative to local governments. This means that in the event of a conflict between state and local government, the state government will typically have supremacy under Dillon's Rule. It should not be confused with Home Rule, which can provide local governments with some degree of independence from the state government.