Arthur Ryland Greer (b. 03 Jun 1920/d. 24 Sep 1995) was my father. During WWII, he told me that he feared being drafted by the Navy due to seasickness (he had an extreme case, and I inherited it from him), so he volunteered in the Army. His sister, Marie Greer (Army), and two brothers, Clary Moore Greer (Navy career officer), and Walter Donald Greer (Army) also volunteered.
About 6 mos into his Army enlistment, he was given a medical discharge due to poor eyesight. Shortly thereafter, he received a DRAFT notice from the NAVY! So he took his Army discharge papers down to the Navy office, figuring they would save themselves the time and expense and go with what the Army had decided.
He presented his Army paperwork to the Naval officer explaining the circumstances of his discharge. The Naval officer promptly snatched the paperwork out of his hands, tossed it in the wastepaper basket and said, "This is the Navy, boy. We'll make our OWN decision!".
Dad was then inducted into the Navy and they did later discharge him for the same reason the Army did: poor eyesight.