I don't know if I agree. Size has some impact. Risking the livelihoods of you and your friends working for peanuts in your bedrooms is one thing, being at the helm of a billion dollar business is a bit of a different beast.
But yeah, it does matter whether you're public or private. A whole bunch of indie games are made by public companies, though. Definitely by corporate-owned companies and companies with big corporate investors.
By that bar a lot of the "indies" being touted here aren't really... that.