Related/Dupe: "23andMe tells victims it's their fault that their data was breached"[0](236 points, 301 comments, 1 day ago) - this article references the that techcrunch article as a source.
This is how you can implement same service while preserving privacy:
1. Customer goes to nearest pharmacy and buys sterile vial and swab.
2. Customer takes sample, writes 30 random numbers on the vial and sends it via mail.
3. Once a month one giant zip file appears on service's website with random numbers and corresponding diagnoses. Customer downloads it and find their random number and corresponding diagnoses.
Pharmacies in the US have just recently been caught giving law enforcement warrantless access to their records, and it's not even illegal. This plan would need some stronger guarantees IMO.
[0]: https://news.ycombinator.com/item?id=38856412