I think you are still conscious during the blackout, you just don't have a memory of it. Amnesia is the effect here, which is a little different than actually being unconscious the whole time.

When in surgery you really are unconscious though, hopefully at least.

I would compare this to forgetting what exactly you did on this exact day and this exact time one year ago. You can't remember it (most likely), but it doesn't mean you were unconscious during that time.