The way it works in Brazil – maybe in other similar countries as well – is that insurance only covers specific doctors which have partnerships with the insurer. A common question when you're talking about a doctor or call his office is "which insurance plans does she accept?". Usually it's 2 or 3 plans, and thus you end up maintaining in your life a network of doctors that work with your specific insurance – so that whenever you have a problem you know where you can get treatment without spending extra.

This creates a relationship where doctors get paid much less than they would normally charge (e.g. $20 for an insurance-paid appointment vs. $100 for a customer-paid appointment). But this way they end up receiving a steady number of clients from the insurer. And in most cases doctors have to accept this deal because they don't have enough demand on their own.

Naturally, that's not the case for top neurosurgeons. They have way too much demand and can make only a few surgeries per week. So virtually none of the top ones agree to being "accredited". They make an order of magnitude more money by charging the customer directly.

If you decide to use a "non-accredited" doctor you have to pay out of your own pocket. Typical insurers won't reimburse you in this case, and even the high end ones will give you back only up to 10 or 15%. They do cover for hospital expenses (room, nurses, meals, etc.), but these are a small fraction of the cost of brain surgery.

There are some different insurance plans that will reimburse your customer-paid appointments/procedures, but – since the cost for these visits is way higher – these are plans that only multi-millionaires can afford.