Wealthy people take a lot of steps to protect themselves against loss. Health insurance is one of many of those steps. A top policy can be had for $10,000 per year and protects not only their health, but their assets. Hospital bills can easily be in the hundreds of thousands, so they have the insurance to protect two things, their health and their assets.
Some wealthy people also make special contractual arrangements with a primary care physician, or specialist in their area of particular need, such as $20-$30K per year for special appointments, no waiting, lots of attention. Such deals are done independent of insurance, paid up front. These are popular among the wealthy in Manhattan. For them, the waste of time is the delay for appointments, waiting, etc, not the insurance. If the doctor is in town, he will see them for the hour or two of their choosing, and reschedule other people's typical appointments for another time.
No, people such as Kobe don't sit down with Blue Cross folders. They have managment companies with skilled people besides their agent, who handle business and personal affairs such as getting a primo health insurance plan.