PICA supplies the dorsolateral rostral medulla. Recall the cranial nerves that have nuclei in the medulla: IX, X, XI,XII. The cranial nerves that control the eye muscles are III, IV, and VI, so we do not associate ocular palsies with vascular insults to the medulla. Obstruction of PICA is not uncommon though, causing Wallenburg syndrome: hoarseness (CN X), dizziness (CN VIII-we say it's in pons, but vestibular nuclei straddle pons/medulla), contralateral  loss of pain/temp (spinothalamic tract), ipsilateral loss of pain in face (spinal trigeminal), ipsilateral cerebellar signs (inferior cerebellar peduncle), ipsilateral Horner's syndrome (sympathetic fibers), and ipsilateral palatal paralysis (CN X). Not what we see here. Return to the case to make another choice.