Final answer:
The false statement is that veins have thicker walls than arteries, whereas in fact, arteries have the thicker walls to manage the pressure of the blood pumped from the heart.
Step-by-step explanation:
The false statement about circulatory systems in the options provided is: "b) Veins have thicker walls than arteries." In reality, arteries have thicker walls than veins because they need to withstand the pressure of the blood being pumped directly from the heart.
Arteries, indeed, carry blood away from the heart, and capillaries do allow for the exchange of gases and nutrients. The circulatory system does play a significant role in the immune response by transporting immune cells throughout the body. Therefore, statement "d) The circulatory system plays no role in immune response." is also false, based on the information but was not listed as one of the provided options.