Yes, he is wrong with his diagnosis. TSH is a pituitary hormone that is affected by so many variables that it is inadequate as a thyroid diagnostic. At best it should be considered as an indicator, to be evaluated along with more important indicators such as symptoms and levels of the biologically active thyroid hormones, free T3 and free T4.
Your wife's FT4 level is below range, and the FT3 level is at the very low end of the range. Both of these ranges are very broad, and many members report having hypo symptoms with similar FT3/FT4 results. You can read more about his on this link.
http://www.hormonerestoration.com/Thyroid.html
In my opinion the best way to treat a thyroid patient is to test and adjust levels of FT3 and FT4 with whatever type of medication is required to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important. Many members report that symptom relief for them required that FT3 was adjusted into the upper part of its range and FT4 adjusted to at least midpoint. If your doctor has a problem with this protocol then you may have to look for a good thyroid doctor that will do so.
One further point is that your wife's TSH result, along with very low FT3 and FT4, may indicate the need to test her pituitary function as well.
Test results with reference ranges:
T4 Free 0.54 0.77-1.61 (ng/dL)
TSH 1.72 0.34-4.82 (ulU/ml)
T3 Free 2.4 2.4-4.2 (pg/mL)
Thanks
It would help us a great deal if you would also post the reference ranges from the lab report. Results vary from lab to lab and they each can have a slightly different ref. range.