Does anything change if my car accident was in a company vehicle?

I was driving a company van for work when another driver ran a red. It was a pretty bad intersection accident, and I ended up going to the ER with a sore back. My boss told me to just file the report with the company’s fleet insurance and they’d handle everything.

But I’m the one who got hurt and I’m the one with the medical bills. Does the fact that it was a company vehicle mean their insurance covers my injuries too, or is that a separate thing? I’m not trying to cause problems at work, but I also don’t want to find out six months from now that nobody was actually handling my side of this.