"Sorry sir your infant child is not eligible for that heart operation due to the genetic marker we discovered in your profile."
And as of 2014, regardless of the nature of the evidence, insurance companies will no longer be allowed to exclude customers based on predisposition to illness or preexisting conditions.
The premise of insurance is that you are insuring against the unknown. If you know that something is the matter with you, then it's no longer insurance. It's getting someone to pay for a treatment that you know you will need. Whether other people should be paying for that is another discussion.
I do think a nontrivial amount of the mess in the health care system is the confusion between the two. People want to create health care plans, but they are trying to make it out of insurance companies, which is going to be problematic at best. Further, people want health care plans but don't want to think about it from an actuarial perspective... because they don't like the answers that come out. That doesn't prevent the answer from coming out, but it does mean we end up trying to build glorious systems that seal themselves away from reality from the get go, and that also can only be problematic at best, total failures at worst.
In fact, HIPAA might have already forbidden that. The law wasn't clear but it's entirely moot now.
[1]: http://www.nytimes.com/2012/11/25/business/seeking-cheaper-i...