Because a government offers funding at a low rate and an entrepreneur takes advantage of such a rate doesn't mean the government "innovated".
I think NASA and the moon are a good example of innovation in the relm of war. The space race was about international posturing and displays of technological capability as a deterrent to engaging in nuclear war. Of course we lost most of the "events" of the space race save putting someone on the Moon.
It seems plausible governments could be innovative as they are comprise of humans and humans can create things regardless of context.
Long scale planning certainly is a strength of a government, because in theory in means funding can be coerced from citizens and invested into projects that they wouldn't normally choose of their free will via the marketplace -- but they often simply don't invest in good long term projects.
Perhaps I'm wrong.. the promise of wealth seems to be a primary motivator, and since governments amass large sums of money through coercive taxation, I suppose they can be a motivational source for inventors and entrepreneurs, but I'm just not comfortable with saying governments are more innovative than individuals.