Seems to me like two different questions:

(1) Should an average person try to study medicine and statistics and find out the answers for themselves, or use an expert opinion?

(2) Are people recognized by current laws / credential systems as "experts" really the best available experts?

I would support people getting information about their health from organizations like 23andMe. But I don't expect 23andMe to do all research on their own -- at some moment they are going to rely on some peer-reviewed study. There should be a system where the studies are not easily gamed by financial interests of pharmaceutical companies, or by pressure on scientists to publish even when there is nothing worth publishing.