Diagnostic tests can do harm.  

They can contribute to unhelpful and potentially harmful interventions by:

Suggesting disease where there is none

Pointing out disease that is not causing symptoms or problems

They can make a person uncertain or uneasy.

The idea that testing can cause harm is counter-intuitive.

Studies of 2 diseases might help make this more understandable: Kienbock disease, and enthesopathy of the extensor carpi radialis brevis origin (aka tennis elbow or lateral epicondylitis).  

Kienbock disease is very uncommon.  It is loss of blood supply to a small bone in the center of the wrist called the lunate bone. No one knows why it loses blood supply. The bone can weaken and even crumble with this problem. This causes pain and stiffness in the wrist. When we diagnose Kienbock disease we have no way of knowing how long the problem has been there or if it will get worse (1). Surgeons and patients tend to treat under the assumption that the disease is active and will get worse without treatment. If that assumption is incorrect, treatments have no chance of helping and can only cause harm.  

Some people who have Keinbock disease do not notice pain or discomfort. Radiographic images of the wrist taken for another reason may identify asymptomatic disease that is in the dormant stage and will not benefit from treatment(1).  

The condition of enthesopathy identifies other drawbacks of diagnostic tests. Enthesopathy is a disease of the attachment point of a tendon or muscle to bone. MRI imaging may be read as showing a “tear” when there is more water or thinning than normal in this attachment point. Even though these changes seem age-appropriate and not an injury (2).

References

1. van Leeuwen WF, Janssen SJ, ter Meulen DP, Ring D. What Is the Radiographic Prevalence of Incidental Kienböck Disease? Clin Orthop Relat Res. 2016 Mar;474(3):808-13. doi: 10.1007/s11999-015-4541-1. Epub 2015 Sep 1. PubMed PMID: 26324836; PubMed Central PMCID: PMC4746165.
2. van Kollenburg JA, Brouwer KM, Jupiter JB, Ring D. Magnetic resonance imaging signal abnormalities in enthesopathy of the extensor carpi radialis longus origin. J Hand Surg Am. 2009 Jul-Aug;34(6):1094-8. Doi: 10.1016/j.jhsa.2009.02.023. Epub 2009 Jun 5. PubMed PMID: 19501476.