How do you determine whether a case study is fraudulent? I had recently read an interesting anthropological case study composed of interviews of Iranians before and after the Iranian Revolution. But after reading the case study, I started wondering whether the interviews actually happened. The case study does not mention the city where the anthropological case study took place, nor does it give the "true name" of the interviewees (instead "nicknames" were used). However, the anthropological case study instead provided a deep description of the city's history as well as biographical information about the interviewees...so it didn't seem that protecting privacy was really important for this author.

I don't want to assume that the case study is a lie purely on gut instinct. So what would be the steps I would need to do in order to verify that the anthropological case study actually took place, and that the author didn't simply make up all the details?
Contact the author and ask for the primary data. Offer to sign any required non-disclosure agreements. I fail to see though how providing information on the history of a city means that protecting privacy was not important to the author. The same for certain biographical information. Indeed, you appear to be adding 2+2 and coming up with 7.  If you have evidence of fraud then contact the journal. Many famous examples of "fake cases" have come to light in the last few years but your reasons for questioning the validity of these interviews (as stated in the question) appears flawed.

EDIT FROM COMMENTS

Do you really think this will be effective?
Sometimes yes,often no. But if you get a flat-out refusal this does give you some additional useful information.

Looking from the point of view of the author, suppose you have pledged confidentiality to your participants, are you really going to be comfortable voluntarily sharing your data with someone you have never met? (Is it even ethical for you to do so?) 
You are making the incorrect assumption my answer says the author will reveal the identities of those interviewed. They should not and will not. What I would like to see are the notebooks or audio files with the interviews that should not contain the names if standard interviewed protocols are followed. For any interview I have done I would gladly give out the redacted transcripts.

*Would any NDA offer sufficient protection? (How would you enforce it, if the requester is in another jurisdiction?) Is it worth your time (and money) to get university counsel to draw up the NDA? *
Your NDA comment is based on the miss-assumption  I am saying the author will give out the names of those interviewed. I did not nor would I condone this. university counsel need not be involved to give out redacted transcripts of interview notes. This is just academic legal-speak. I would just draw something up asking for my notes to not be used for anything I do not want them to be used for.

Wouldn't it be much simpler and safer to just say "No"? Yes, but isn't it always when someone makes a request of your data or similar. In my experience quality academics have always made an effort when I asked for something.