These hormones and their interconnectedness are quite complicated in al their details. TSH is not only connected to the regulation of T3 and T4. TSH receptors are found elsewhere, not least in the brain itself.
Then TSH is released pulsatively, with circadian changes as well as seasonal, and generally increases with age, is affected by illness or other stress. That is a huge range for confounders on the measured numbers and correlated effects.
Put simply, TSH will likely not be the direct cause for fatigue or tiredness, but is in many cases an indicator of thyroid problems, signalling that only with elevated TSH the T3/T4 levels are kept in the desired range, for now. Since this is about a tight feedback loop the initial reasoning in the question seems to be incomplete in this regard.
Given the limited information available from the question, the most likely answer seems to lie in this explanation:
The pituitary TSH-producing cells are inhibited by T4, which is taken up by the cell and deiodinated intracellularly to T3. Under normal conditions, the inhibitory effect is primarily exerted by the circulating T4. This is illustrated by the fact that in primary hypothyroidism, the TSH concentration increases early and is inversely related to the falling T4 concentration.
The T3 concentration is affected to a lesser degree (often not at all) in early stages of primary hypothyroidism. Normal T3 concentrations are maintained in such situations by an increased conversion of T4 to T3 instead of reverse T3 (rT3). Low T3 concentrations are therefore only seen in more pronounced hypothyroidism. Analogous to this, a slight increase in T4 can result in reduced TSH release in spite of normal T3.
The high analytical specificity attained by the modern TSH methods (based on monoclonal antibodies) can cause problems. Circulating TSH is heterogeneous. Different TSH methods can therefore determine various immunoreactive parts of the TSH populations in patient samples, which results in different reference ranges for healthy people, depending on the TSH method used. In addition, the immunological methods can be affected by interference. The most significant interference for TSH determination is caused by heterophilic antibodies. Animal antibodies, such as human antimouse antibodies (HAMA), in patient samples can create the bridge that is normally formed by the analyte (TSH) in the analytic reaction, thereby giving a false increase in the TSH value. Heterophilic antibodies occur in low concentrations in about 50% of the population, but the effect of these are eliminated in routine diagnostics by addition of immunoglobulins from nonimmunized animals or humans. In cases where it is diffcult to interpret the results (unexpectedly high/low TSH values) the laboratory should be consulted.
(Ernst Nyström et al.: "Thyroid Disease in Adults", Springer: Berlin, Heidelberg, 2011, p 18.)
That leads to the following conclusion:
While screening patients for thyroid disease, physicians often find increased thyrotropin-stimulating hormone (TSH) levels in patients whose free thyroxine (T4) levels are not below normal. This state, termed “subclinical hypothyroidism,” is most commonly an early stage of hypothyroidism.[…]
The likelihood that this will happen increases with greater TSH elevations and detectable antithyroid antibodies. Because patients with subclinical hypothyroidism sometimes have subtle hypothyroid symptoms and may have mild abnormalities of serum lipoproteins and cardiac function, patients with definite and persistent TSH elevation should be considered for thyroid treatment.
Subclinical Hypothyroidism: Deciding When to Treat
(Victor Adlin, M.D., Temple University School of Medicine, Philadelphia, Pennsylvania,
American Family Physician. 1998 Feb 15;57(4):776-780.)