In an interview with Robert Utiger, who developed the TSH test in the early 1980's, Utiger explains why the TSH result does not always reflect one's thyroid status. In fact, patients with a low TSH can be hyperthyroid, hypothyroid, or euthyroid.  TSH is also most likely to be low in patients on T3 or glandular replacement hormone.

Utiger also explains that TSH concentrations are also undetectable in patients with various types of thyroid autonomy. While he doesn't mention Graves' disease, twenty years ago, the American Association of Clinical Chemists reported that TSH is frequently misleading in patients with Graves' disease.

In the clinical laboratory, the TSH test is recommended as a screening test to look for thyroid disorders in the general population. In most cases, a low TSH suggests hyperthyroidism and an elevated TSH suggests hypothyroidism. However, although they're not common their are a number of exceptions to this rule particularly in patients with Graves' disease, patients with atrophic autoimmune hypothyroidism, patients on thyroid replacement hormone, patients with central hypothyroidism (low TSH) and individuals with TSH-secreting tumors (high TSH). 

 Resource: Thyroid Patients Canada. "A Dialogue with Utiger: T3-based thyroid therapy over-suppresses TSH." Sept 10, 2019  https://thyroidpatients.ca/2019/09/10/a-dialogue-with-utiger-t3-over-suppresses-tsh/