Final answer:
Governing boards are indeed responsible for ensuring an organization fulfills its mission, which is true. However, proprietors in a proprietary colony had more responsibilities than just to collect profits. Local governments are constrained by Dillon's Rule, and colonial governors had veto power.
Step-by-step explanation:
The statement that governing boards have the ultimate responsibility for ensuring an organization serves its mission is True. Governing boards, such as boards of directors in corporations, are tasked with overseeing the organization's management and policies to ensure they align with the mission and objectives.
This includes setting strategic goals, hiring and supervising top executives, and ensuring that the organization complies with legal and ethical standards. In the context of a proprietary colony, however, the responsibilities of the proprietors include not only collecting profits but also managing and governing the colony.
Dillon's Rule implies that local governments have only those powers expressly granted to them by state law, which is often quite restrictive, so the statement regarding Dillon's Rule giving local governments freedom and flexibility is False. Lastly, colonial governors did possess the right to veto legislation, which is True.