I saw this on the Let Fat Be Thy Medicine. I hope they won't mind my shameless promotion of their movie by using this pic.
Here's my 2 cents worth of thought on the issue: No it's not and no you don't. What may be "killing" your thyroid is a poorly formulated low carb diet - just like any poorly formulated diet might. But it ain't the lack of starch, as starch is non essential to human life. The lack of what you don't require can't make you deathly ill.
I said it before and I'll say it again: obesity is not caused by eating too much food per se. It's caused by the type of food you eat and how the food you're eating affects your hormones.