I can't say that I agree with the info from that source entirely. While it is possible to be hypo due to iodine deficiency, that is very rare in most developed countries due to the use of Iodized salt. Most of our food has Iodine in it.
Supplementing with Iodine when you don't need it can cause problems. It can cause you to go hyper, it can cause you to go more hypo, or it may do nothing at all. Also I can't recommend suplementing Iodine without supplementing Selenium.
On the subject of the Thytrophin, I Can see how it might help, if a nutritional deficiency is what caused the hypothyroidism. Often, that is not the case, and this supplement probably wouldn't help some people, but woudl make a difference for other.
I am all for supplementing and trying to correct andy health problem through lifestyle and nutritional changes first, and believe that doing that in an educated manner, knowing that something may or may not work can sometimes yield some surprising results. Knowing that, maybe you could try their advice. You have nothing to lose except some time and money, and stand to gain your health and freedom back (no more daily pills is only a dream for me).
On the other hand, one site that sells Thyrotrophin says this:
Thytrophin is used to help support normal thyroid gland activity. It has no hormones within it and therefore will not replace Armour thyroid or Synthroid
SO, if your hypothyroidism is not caused by a deficiency of something in Thyrotrophin (i.e. antibodies have destroyed it, it has been removed, etc.), then it can't help you.