"Genius"? Where, exactly, did I say that? You are putting words in my mouth.
Anyone who gets that high in politics is smart enough to think up something such as Medicaid. The argument that LBJ is too stupid to think up Medicaid by himself lacks complete substance.
LBJ's Great Society was based in part on both FDR and Kennedy's programs. Bill Moyers and Richard M. Goodwin, two of LBJ's assistants, and their committees had a great effect on LBJ's programs.
However, Medicaid/Medicare in and of itself was not something FDR did nor LBJ did do it by himself.
The Social Security Act of 1965 actually had more of its origins with Truman's administration. Truman was the president who approached Congress about starting a national health care program. There were debates about various proposals through the following years in Congress, the Social Security Administration, and the Medical Industry. In 1965 a bill was passed and then signed by LBJ's administration.