If the insurance company has any defensible path to denying a claim, they will take that path. If your policy says that your coverage is invalid if your medical lapses, then they will try to deny the claim based on that, regardless of whether it was legal to fly the airplane. If the insurance company actually tells you that the FAA's extension means you're covered, then that's another thing.
The way most (all?) federal regulations work is that the federal government can commit not to prosecute for a violation related to a specific issue, but states with delegated authority are not obligated to respect the federal government’s commitment.
In my business career, there were situations wrt to environmental regulations where the federal government committed not to prosecute but a state was unwilling to make a supporting commitment.
I think it was either AvWeb or AOPA who posted an article the other day explicitly pointing out that, while the FAA may not be enforcing your expired medical, your insurance company can (and likely will, unless they've stated otherwise) consider flying with an expired medical a violation of the terms of their coverage, and not only would they refuse to cover a loss under those circumstances, you likely could lose your coverage altogether if they find out about it.
Yes, the FAA can say anything they want about your medical, including waiving enforcement for now, but the insurance company is a private organization and not bound by the FAA's actions.
The recommendation of the article (I wish I still had a link) was that you check with your agent and, if they're willing to extend coverage when your medical is expired, get that in writing immediately. Do not just take your agent's word for it.
The beauty of the system is all you need to do is start the red tape moving. If your D.R. will see you, once the exam is in the system, you are covered. It will have a date. Issues of the FAA processing it is a complete different problem. They are essentially giving themselves a pass.