23 And Me should only have to prove that it is better than the alternative, not that it is accurate (to determine whether the service is of net benefit to the public). Depending on the counter-factual, 23AM could provide a relatively inaccurate test that would still be better than no test.
Unfortunately for us, the FDA is on a quest for "safety"; the agency does not try to help the citizenry live longer or happier.
http://www.bmj.com/content/333/7562/284
For screening tests where the problem being screened for is rare, most results will be false positives, but the result is not intuitive.