David is totally correct in this regard. However it can be very hard to convince a producer that you arent technically "freelance" when they are hiring you.
There are a few types of insurance to consider here:
-Equipment insurance. There are a variety of companies that can cover your gear. Peruse the forum. Many operators are signed up with WP Dolle. You have to joing the Steadicam Operators Association in order to get a policy with them.
-Business liability insurance. I use Hartford to insure myself / my business, very easy to work with them.
The production should absolutely issue you a COI for your gear. Whether or not your gear is insured by yourself, the production company should be able to sow you proof that they have insurance that could cover your gear in the case of a loss / claim. THAT BEING SAID-A COI IS NOT A CONTRACT AND ENTITLES YOU TO NOTHING. There is always a battle when bringing a claim to the producer on their insurance, but it is there for a reason. They should not hesitate to give you this. IT ONLY APPLIES TO YOUR GEAR.
To work on most sets, you are supposed to be covered for workman's comp, which usually is the responsibility of the payroll company. However, if you are working as a vendor (I used to have a contract with Kohl's where I would rent gear and hire crew and was brought on to the shoot like a production support company-thus a vendor), you will sign a contrcat that will necessitate that you are insuring yourself and your hires.
In Los Angeles, you have to register yourself with the Los Angeles Tax Commission whether or not you are an LLC, SCorp, etc. Its a pretty simple process. This will make you a "business" in the eyes of the county. Then you can set up an LLC in the state.
The way that the producer is framing it, makes me think that hes telling you to be a loan out of your company, as if both you and your equipment are loan out. which could be possible, but it doesnt actually insure you. it just masks the requirement of your person being insured.
Many of these insurance companies will also provide short term (1-day or more) coverage. It is expensive, but can be helpful in a pinch.
Get used to and ready for insurance. Nowadays I think I have almost ten different kinds-health, equipment, homeowners, car, business, umbrella policy, etc.