The Short Version
Standard anatomy sources support the claim’s central point: parasympathetic outflow is conventionally taught as craniosacral, arising from brainstem nuclei and sacral segments S2-S4. The main caveats are that this description applies most precisely to preganglionic parasympathetic outflow, not all parasympathetic fibers, and that some modern research disputes whether the sacral outflow should be labeled parasympathetic at all.