I am not going to knee-jerk and say the T-3 claims are a myth. I will say, however, the claims all stem from early investigation from studies like: (Res Vet Sci 1981 Jan;30(1):7-13) that did report lower thyroxine levels in sheep treated with Tre.n to increase lean meat production.
The problem is that (at least in ruminants) thyroxine levels drop with just about any steroid NOT just tre.n. It is hypothesized to be one of the reasons fat % drops, increasing relative lean meat in stock and is why estradiol is often added to the mix.
So if the taking of T-3 should be a recommended practice with tre.n, so should it be with ALL high adrogenergic steroids. In theory, anyway.