Actually, it wasn't a joke. The Navy has more than one army, and their biggest army is the Marine Corps. The Marine Corps has its own air force. The Marine Air Force actually has a few carriers of their own, although the carriers are part of the Navy and manned by sailors.
John Paul Jones is a great American naval hero of the Revolution. But the new US did not have a navy. The US Army had some ships, however.
During the 1950's the US Air Force had a series of satellite tracking stations that ran down the Caribbean, but the series couldn't track far enough. The Air Force procured two surplus WW2 Navy ships and converted them to tracking stations. When Eisenhower was President, that was one of his reasons for forming NASA and moving all the space development into one department.