It sounds a little shady, or at least impersonal or careless for the interviewers not to inform you that you were being considered for a different position. It sounds like you have the training and know what you want, and don't want, but they don't consider that to be relevant. If you don't want to move, and you are sure that you want job X, then you have nothing to loose by standing up for yourself (unless you suspect something sneaky, like getting downsized out of a job or let go). I'd write the letter and be firm yet polite, so as not to burn bridges. JMHO

Mostly because of that "it's a small world" factor.

I'm not sure why you would not have said something to them during the interview if you knew it was not the position you wanted. I guess I am unclear on that part.

There is absolutely nothing wrong with saying you were only interested in position X.

How did this all go down?

the various aspects of the job including the title and responsibilities. Good luck.

And make it clear that you would not relocate for position Y.

lots of good advice in this thread. learning to be good and kind to yourself after an interview gone wrong is harder when you've been searching and hoping. i hope our vibes and good wishes move the bad aura from that company for you.

If they come back and offer Y, explain that you're not really interested in Y because you have other options that would be less disruptive to do Y locally and reiterate that you applied for X. Job hunting is not always fair-sport. If you can get away with it, it's not out of bounds even to imply that you have more-prestigious/better-paying/more-local options to do X but were more excited for the possibility to work for them than your other options.

It's how I got my first NPO sector job. There was no other option on the table for me and they'd offered me an equal-level (slightly-higher-pay) computing position I had not applied for and was not interested in despite being exceptionally-qualified for. I declined, inferred I had another option for the organizational-role I wanted but a preference towards them and put them in the position of choosing between hiring me for the position I wanted or not at all. They hired me. (It was admittedly a leveraged-gamble that I was the best candidate for both positions; there was no question I was a better fit for the position I didn't want. There was also no question for me that I wasn't accepting their offer. They were either going to have to offer me the position I sought, make me an offer for the other position that simply blew me away or they weren't going to get me. Like you I was trained well beyond the level of someone for the position I sought but lacked experience.)

I wasn't going to take the position I didn't want and it was not my problem they had a lot of interesting applicants for my job and zero for the position they wanted to offer me.

If you have marketable skills, and the willingness to use them, you should be able to do well.

Another possible aspect to consider is that companies tend to have economic reasoning processes. The people involved sometimes tend to narrow their views to support that short sightedness. You seem to have much more of an emotional buy-in, (as you would). It might be worthwhile to start having more of a similar attitude to theirs. That would mean discarding loyalty, and continuously marketing yourself for a better position. Although my career field is probably very different than yours, that approach has enabled me to increase my income ~300% over 6 years.

As far as the e mail goes, word it carefully. Thank them for the consideration. And point out that you were hoping to use your new(?) skills in a more challenging job.

In any case good luck, happy hunting, and remember - You kick ass!