Sometimes driving a state vehicle is why she asked for the license of course, and maybe she asked for insurance proof because it is required to carry insurance to have a valid license.
Yes, I know how that sounded. 
Since when do I need insurance in order to have a valid license? If I drop my auto insurance, the state demands that I turn in the vehicle’s license plates, not my driver’s license.
Not even that much in California. You’re required to have proof of insurance to register your car annually, but in-between if your insurance lapses or is canceled nobody is going to come knocking at your door asking for your registration.
No, it’s not.
At least, not in Illinois.
I didn’t own a car for the better part of a decade when I lived in Chicago, but my license remained entirely valid. The only hitch was that when I rented a car I had to purchase their insurance, but since that was infrequent it was cheaper than maintaining year-round insurance for a car I didn’t have.
Danger, Will Robinson, Danger!
This is totally unreasonable. It is also a symptom that Something Shady May Be Occuring.
I strongly suggest you either take this to the next level (Ms. Bitch’s supervisor or the human resources/personnel department at your place of employment) or get another job. People involved in unethical/illegal activities are happy to drag others, particularly subordinates, into the mess. The “don’t question, just obey”, threats, and demands for personal information are not good. Protect yourself.
This does indeed happen, at least on some campuses. It seems to me to be a reasonable attempt to limit liability.
I seems like having insurance should not be a requirement to drive a state car. After all, someone might not own a car but be a licensed driver.
The manager seems to have mishandled this situation, unless there is some important factor missing from the story. Maybe she is in hot water for having let the OP drive a state vehicle without getting the required info first, and is now in panicked CYA mode? That still doesn’t excuse her from explaining why the info is needed, though.
While they won’t come knocking, the DMV will send you a notice and subsequently cancel your registration if you don’t have insurance. All insurance companies are required by law to transmit policy status to the DMV (this is why you can renew your registration over the 'net without sending in your insurance card) so rest assured the days of buying insurance solely at registration time are over.
You could stir up trouble, probably. But think about the big picture, as it impacts you.
You’re a student assistant. This is not likely a full-time career for you. Nor a long-term one. Unless you’re like some SDMB’ers and still working on that thesis 20 years after taking your last course…
If your insurance doesn’t cover you, let them worry about it. You’re not going to commit your insurance company to anything they don’t agree to be committed to by providing the insurance info. Just give them the info (as you already have) and don’t worry about this. It has no net effect on your job, your insurance, or anything else. Be like a willow tree, and bend, not break.
Any updates?
This is almost surely the best advice. Life is full of injustices and petty annoyances, you must learn to choose your battles carefully if you have any hope of winning in the long run.
Yeah I decided just to let it be.