What I wrote was directly talking about Patient 2. Normal free T4 and normal TSH in a hypothyroid patient on T4 replacement can be found without resolution of clinical hypothyroidism. In other words, the lab studies can be completely normal after T4 replacement and they can still be clinically hypothyroid.
T3 is the 'active' form of hypothyroid; While T4 does have some activity it is far less than T3. Most Hashimoto's patients have a high degree of antibodies to Thyroid Peroxidase--the enzyme that converts T4 to T3. Which means even on T4 replacement, normal free T4, and normal TSH, that they aren't converting enough T4 to T3 to have truly normal thyroid function.
Thus, augmenting with T3 makes sense, even if by lab studies alone their hypothyroid appears to be adequately treated. You are not only engaging in an appropriate treatment for depression, but possibly treating a medical cause of depression. You need to coordinate with the prescriber of T4 because generally speaking you need to drop the T4 dose by 25-50mcg when adding T3 on to prevent iatrogenic hyperthyroidism.