The diaphragm is sort of mix of skeletal and smooth muscle activity, though it is an exception to the rule that smooth muscle is all involuntary. Difference sources cite it as different muscle types but the general consensus is that its skeletal muscle. The reasons behind it are detailed and you won't even delve into it much in med school, but essentially one can break the diaphragm into 2 different muscles innervated by the Phrenic nerve ("C-3,4,5 keeps the diaphragm alive" sticks with me long after MS I). The result is the diaphragm can be consciously controlled, but eventually it will contract and extend on its own and is generally functioning w/o any conscious input. The muscle itself does have somatic innervation.
The autonomic NS also plays a role in diaphragm activity. The contraction of the diaphragm during inspiration requires sympathetic nervous system (SNS) input to fire the contraction and resultant contraction/flattening of the diaphragm. This draws the lungs down and allows air to enter the lungs. Expiration involves switching off the SNS driven contraction, allowing the muscle to rebound back to its original position. This is driven by parasympathetic NS activation which acts as opposition to the SNS.
In 10 years, I have yet to see the AAMC test material in this manner (much like asking if viri are considered"alive"). They like to avoid these kinds of gray areas because it would be hard to have 1 clear correct answer in a given scenario. If they do want to delve into new areas, they will most likely do it in the passage.
