TL;DR: If you are reading this review, and have read others that knock the show as being a trope or rote, please note that if the tv show sticks close to the source material, this will be a story that you have never seen or heard before - it's truly brilliant, unique and you should watch till the end. As to the complaints about the sheriff, read below for context that others have missed.
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Having read the books, I completely understand why the husband doesn't investigate the birth control issue.
The people of the Silo have been taught from birth that the rebellion almost destroyed them all and that their elders (those in authority) are trying to protect them - which is made clear in the freedom day celebration in episode 1.
The people of the Silo accept whatever they are told as fact and true - they are innocent of concepts like conspiracy, and they trust their leaders completely and without hesitation.
So, when the doctor tells the sheriff that the item in his wife's body was a "placeholder" or to "prevent infection" (his wife says this while in jail), the sheriff accepts this over his wife's theories because he truly and simply can't even begin to imagine that someone in authority would ever deceive him/them.
In many respects, the Silo inhabitants are like children in their understanding and acceptance of things.
Perhaps the tv adaptation needed to do a better job of showing how the people of the Silo are completely brainwashed into believing authority and why. That said, I think this is a great adaptation so far and I can't wait for more.
I'm also taking off a star because I personally dislike profanity on TV and it irked me that this show had it.