I think the risk of a blood draw has to be just about as close to zero as one can reasonably get.

It's not the blood draw, it's false positives resulting in unnecessary expensive and frequently invasive procedures done. A quick Google search for too much screening provides many results on the topic.

I think that's hyperbole at best.

Tell your hypothetical idiot doctor about the new guidance coming from the CDC and watch how fast he shuts his stupid hypothetical mouth.