Regarding epiphanies: if an idea "comes to me" and it's not something I was really thinking about, but it's really novel or useful, is it really MY idea?

There's your consciousness, and then there are sometimes random thought that are subconscious. If a thought comes up without you trying, and you discover or create or do something good, can you really claim that is was you, or just some background type thing in your brain, more due to genetics than your personality or free will?