Final answer:
The statement is false; both the sympathetic and parasympathetic nervous systems typically innervate the same organs, providing dual innervation for the regulation of homeostasis.
Step-by-step explanation:
The statement that body organs are innervated by either the sympathetic nervous system or parasympathetic nervous system, but not both, is False. In reality, the autonomic nervous system, which includes the sympathetic and parasympathetic divisions, typically provides dual innervation to organs. This means that both divisions can, and usually do, innervate the same organ to maintain body homeostasis.
For instance, the heart receives connections from both the sympathetic and the parasympathetic systems: the sympathetic system can increase heart rate, while the parasympathetic system can slow it down.
These complementary functions are essential as they allow the body to adapt rapidly to varying environmental and physiological demands, exemplified by the 'fight-or-flight' response triggered by the sympathetic nervous system and the 'rest and digest' response facilitated by the parasympathetic nervous system.