I've been thinking about this a little more, and this is what occurred to me:
Very intense training leads overtraining, many of the symptoms of which closely mimic hypothyroidism.
This suggests that overtraining might mess with thyroid function. A search on Google Scholar confirms that overtraining is linked to thyroid dysfunction:http://scholar.google.com/scholar?q=overtraining+syndrome+thyroid+function&hl=en&as_sdt=0&as_vis=1&oi=scholart&sa=X&ei=7z4NUZ3iIOnV0QHBk4HoCA&ved=0CC8QgQMwAA
So an athlete that trains very hard for a long period of time may suffer from hypothyroidism. If you look at Salazar's history as an athlete, it sounds pretty likely that this happened to him. Now if you overtrain, you can go to the doctor and get your thyroid hormones checked, and they're probably low. So he prescribes synthroid or whatever, you take it, and now you can continue training at the high level you were at before, only you won't overtrain. There's other issues to worry about -- can you raise low testosterone with thyroid hormones? I don't think so, though I'm not sure. You'd have to look into other methods to legally raise testosterone. Anemia may also be an issue. If you want to fight this legally, you supplement with iron+ Vitamin C and live at altitude, which legally raises EPO levels. So basically, a "clean" athlete who trains scientifically tries to get the benefits of PEDs without actually taking any banned substance.
It's interesting that a number of people known for training extremely hard are hypothyroid, isn't it?