When I was much younger, I worked for a couple companies that had (what I would consider) large fleets of vehicles, and they all were insured through an insurance company. I guess I just assumed that's how it was. I wasn't aware self-insuring was a possibility. Thanks.
Often self insure means they still pay an insurance company to handle the paperwork, but when there is a claim the company pays it.
For health care, a lot of large companies technically have say Anthem or whatever but the company pays out all of the claims and it's just administered by Anthem. So you may have seen a similar thing where all claims were handled by say Geico but it's not Geico's pot of money paying out claims.