The idea of the indie game (at least, as a term to describe a definite sector of the industry) was mostly a new concept when the 360 was in its heyday. We owe the rise of the humble indie title to the power of the internet; between the emergence of Steam, PSN (PlayStation Network), and the Xbox Live Arcade, game development became accessible to anyone and everyone.
Companies like Microsoft and Activision did have a hand in publishing some of these games but, in the beginning, they played a crucial part in getting the ground running. Some involvement from big publishers was often a necessity for the indie games of the 2000s, whereas now this sector of the industry is much more self-sufficient.
Recall [Indie] [Jtag RGH]