I think they mean where none of the crew were state-sponsored astronauts; i.e. fully private.
Maybe there’s something wrong with me but I’m just disinterested in this. I’m a life-long space nut, I’ve read scores of books about the US and Soviet space race. I dream of the day when we colonize Mars and beyond. But for some reason this flight doesn’t seem all that magical to me, or special. NASA missions feel like they belong to all of us (in the USA at least) but this doesn’t. Maybe that’s why this doesn’t feel like anything special to me. I wish it did.