They explicitly state that the patient has been taking excess of his levothyroxine medication. Levothyroxine is the exogenous form of T4. Therefore, free T4 must be elevated. T4 is converted to T3 at most peripheral tissues, so T3 will also be elevated. Because the body has more thyroid hormone than needed, less TSH will be made, and the thyroid will be less active, taking up LESS iodine.
Taking excess Levothyroxine will cause, Incr fT4, Incr fT3, decr TSH, decr Thyroidal iodine uptake. Excess liothyronine intake will cause incr T3, Decr T4, decr rT3, Decr TSH, because T4 gets converted to T3 and rT3 in periphery.