I normally avoid citing Wikipedia as a source, but here is what it says about his military career (emphasis added)
Kennedy enlisted in the United States Army in June 1951, signing up for an optional four-year term, which was shortened to the minimum two years after his father intervened. Following basic training at Fort Dix in New Jersey, he requested assignment to Fort Holabird in Maryland for Army Intelligence training, but was dropped after a few weeks without explanation. He went to Camp Gordon in Georgia for training in the Military Police Corps. In June 1952, Kennedy was assigned to the honor guard at SHAPE headquarters in Paris, France. His father's political connections ensured that he was not deployed to the ongoing Korean War. While stationed in Europe, he traveled extensively on weekends and climbed the Matterhorn in Switzerland. He was discharged after 21 months in March 1953 as a private first class.Ted Kennedy From Wikipedia, the Free Encyclopedia
Seems like the requirements were met.