Final answer:
The apneustic and pneumotaxic centers in the pons are true modulators of the medullary respiratory output, with the apneustic center controlling the depth of inspiration and the pneumotaxic center regulating the rate.
Step-by-step explanation:
The statement that the apneustic and pneumotaxic centers in the pons may modulate medullary respiratory output is true. The apneustic center promotes deep breathing by stimulating neurons in the dorsal respiratory group (DRG), hence controlling the depth of inspiration. On the other hand, the pneumotaxic center inhibits the DRG's activity, facilitating relaxation after inspiration and managing the breathing rate. These centers in the pons work inconjunction with the medulla to regulate involuntary control over the breathing muscles, ensuring the body's demands for oxygen are met.