Seems it happens a bit... and often not from where you'd expect to find it. Yes, Americans are quick to forget their are five branches of the American military.
Here's a little bit about the corps of cadets at Norwich University:
Military colleges have a long and proud tradition in American history and were not designed solely for students planning military careers. The Corps of Cadets prepares students to become competent and responsible citizens. Norwich, established in 1819, was the first of all private military colleges in the country. Our founder, Captain Alden Partridge, understood that structured military lifestyle combined with rigorous academics would benefit those pursuing careers in both the military world and the private sector. His vision resulted in the creation of the Reserve Officer Training Corps (ROTC). As the birthplace of ROTC, Norwich houses all four branches of the armed services—Army, Navy, Marines and Air Force. Our Corps of Cadets program allows individuals to gain military experience while earning a degree.The reason this one pains me so is that if any school ought to know better, it's Norwich University. Afterall, the university's president, Dr. Richard Schneider, holds a commission as a general officer in the Vermont Militia... and is a retired Reserve flag officer... from that fifth branch of the American military.