Wealthy people do not usually carry health insurance. Most might have a catastrophic but often just self insure.
Perhaps she decided to go public with all of this because she knew she would NOT be able to keep it quiet. One way or another, her medical records would be leaked/sold to the tabloids and she wanted to avoid that.
I remember when Farrah Fawcett was dying of cancer, her medical records were sold to one of the tabloids by a hospital employee (who has since died via, I think, suicide).
True, this will be all over the tabloids anyway, but I think Angelina was wise to speak out and perhaps take some of the wind out of the tabloid’s sails.