I would NEVER patronize a doctor who sent my blood to Theranos. At the time it was operating in Arizona, it was only after a tremendously intense and expensive lobbying campaign to get approval. That was very much in the news at the time.
This doesn't make sense. You are just getting your blood drawn. You don't even see who is doing the test until it's done. How on earth would you even know.
Is your doctor the one who actually takes your blood and sends it in for tests? Where I'm from, the doctor just orders a blood test, and you go to some other lab facility somewhere (with some discretionary choice) and get it done by a phlebotomist and its more or less outside of the doctor's purview.