Normal TSH Levels in Hyperthyroxinemia
Since you're asking about hyperthyroxinemia with normal TSH serum levels, I suppose you're talking about euthyroid hyperthyroxinemia.

In euthyroid hyperthyroxinemia, the serum T4 and T3 concentrations are increased, but the TSH concentration remains normal. Besides that, there are normally no clinical signs.

The cause of that increase, as you explain in your own question, is a mutation in a transporter protein (like TBG), or an increase in their concentrations (which can happen in patients with hepatocarcinoma, for instance).

However, the free T4 concentration remains the same, and that is the important value for the negative feedback mechanism that regulates the concentration of TSH:


  The euthyroid status of subjects with FDH has been
  confirmed by normal TSH response to TRH, normal free T4 concentration
  measured by equilibrium dialysis using appropriate buffer systems, normal T4
  production rate and normal serum sex hormone-binding globulin concentration.


Thus, without an increase in free T4 levels, there will be no drop in the TSH concentration.

Source: Impaired Sensitivity to Thyroid Hormone: Defects of Transport, Metabolism and Action.