All we know about this institution is that it is a "very fine arts center". Even if you think you have have taught in a similar place, there is no way you can compare insurance experiences or policies.
If this institution has valuable art on display, and education is not their primary source of income, then obviously their general liability insurance would be different than for a school.
If this arts center is primarily a school, then is it part of the public school system? Here again, the general liability insurance would be different than if it was a private institution.
Regardless of whether it is a school or a gallery, whatever the institution's insurance company says, is what the institution must do, or else they will need to find another insurance carrier.
Why blame the institution for the rules given them by their insurance company, just because you never before encountered the situation where you were asked for a certificate of insurance? For most businesses in this country, it is a cost of doing business.
Maybe their insurance is so costly, they cannot afford to pay for the insurance of their "independent contractors". Furthermore, an independent contractor might pay much less than the institution would pay for the same insurance coverage.
An example would be if the institution charges you for their cost of the extra insurance they must buy for you to be covered on their premises, and if you can buy it cheaper than them, then you earn more money if you buy your own insurance than to buy it through them.
For those of you who have never provided your own insurance, I suspect the overhead cost of insuring you while on their premises was accounted for in the amount they offered you for compensation. Yes, I'm saying you paid for your insurance and you didn't know it, because it was in their overhead and you do not control what they can afford to offer you.
You can see why someone with a stream of teaching income might find it convenient to be able to provide their own certificate of insurance whenever they get a teaching job, instead of trying to obtain insurance whenever they get a job requiring coverage.
The high cost of insurance has put many institutions out of business because you cannot operate without it.
There is no other industry that operates on such a huge discriminatory basis as the insurance industry. Their underwriting process makes the FBI's profiling techniques look like a child's game. For a general example, they know the percentage of people in a city who are negligent, who will sue them and the percentage that will commit insurance fraud .....and this is only a drop in the bucket of information on which they base decisions about the policy they are writing for you.
No one is equal in terms of insurance. You are judged on things that have nothing to do with you or your work. And it all changes when you move to another place, even within the same state. The more you know about it the more insane it appears.
That's why some folks can easily and affordably obtain insurance and other folks cannot. The profiles around you determine everything about the cost and availability of your insurance.