Do you trust them to use your data appropriately and act in your best interest?
No your best interest, but their. The data of your disease could be used by another insurance company; that is to say, if you had operation then changed job, the private health insurance of the new company would not cover your disease. It happens like that in my country.
Yep. And there is no telling what laws change down the track, so giving permission now will grant permission forever, regardless of what changes.