I'm having trouble understanding how you feel this is immoral. You have a private healthcare system, and as such your data is already in the hands of numerous private companies. From the hospital itself, to various data processing partners that implement patient record systems, billing systems, image processing for various tests, lab companies and so on.

But suddenly this company, Google, makes it immoral? It seems to me that if you care this much about private companies having your data, you should switch to a publicly owned healthcare system.