There have already been cases of women refusing to be screened for a known gene that predicts breast cancer because they are concerned that the health insurance companies might get the information and drop them from coverage. BRCA1 is just one example. The genomics research community is discovering new gene/disease associations more rapidly every year. Within the last year, two different genes have been shown to have association with age-related macular degeneration. This is a very powerful tool in the treatment and diagnosis of disease. Still there is a great fear about using this tool since the insurance industry would certainly want to use it to increase their bottom lines.
I think that a key issue here is personal control of information. There are already some efforts to control who has access to patient information and when (HIPAA, meant to protect patient privacy but also, I think, an anti-insurance spying tool). Insurance companies should never have direct access to patient's confidential information and this would include the results of any genetic tests. It is already pushing the issue to ask a patient to fill out a screening form before offering coverage. Yes, you can refuse to answer, and they can refuse to cover you.
I am a scientist. It is difficult for me to see what could be such a potent and powerful tool for the better being debated about what would happen to the $$$ of insurance companies if they got the information. I don't have a ready-made solution for how to solve this. Of course, I can do my own genetic screening in my lab, so no one but me would know the results.
I'm talking about single or several gene screening here. It is pretty easy. Takes 2-3 hours and costs about $25. Whole genome scanning is still a few years off from being universally affordable. A genomics colleague says that it should be under $1000 within 10 years.