I would not want anything changed based on those low free Ts. Even the total T3 is too low!
I might be able to buy her argument about bone health if I knew for a fact that TSH was necessary for building bone or preventing its loss. But I think you can see as easily as I how patently absurd that argument would be. Bone loss is based on T4 and/or T3 that's too high, not TSH too low; since your Ts are nowhere near "high", you will not lose bone if your meds stay the same. In fact, you probably need an increase, not a decrease. (Also, bone loss is just as likely when the Ts are too low as when they're high.)
For a reason I can't explain, Armour very often suppresses TSH. I've never been able to find a documented reason why this is so, but if I needed proof to take to an MD, I'd consult with the people at Armour. I think I read here that someone did that... was able to talk with an RN or something. Anyway, there's the place to start.
You may already know that my TSH is also suppressed... has been .01-.02 for about 3 years now. My MD is perfectly fine with that; he doses based on the FTs.