Where did this snowclone, of the Wiltshire snowclones, actually come from?

Solution 1:

It is certainly not made up by the podcast. Let me start by explaining the saying when it's not being used ironically or sarcastically.

Back in the day (100+years ago) in Britain when people didn't move their home around much, and there was a strict class system, most areas of the country had a few prominent upper-class families. If you met someone from that area with that name you could reasonably bet they were related to the family. For example if you run into someone called Edith Crawley in Yorkshire they are probably related to the Crawley family. If you are yourself upper class you probably know someone from that family and this gives you an immediate connection.

However family names are not unique, so if you were to run into someone called Edith Crawley outside of Yorkshire they might or might not be related to that family. To establish if this is the case, when they introduced themselves you would traditionally ask "of the Yorkshire Crawleys?", meaning "are you related to the prominent Crawley family of Yorkshire?". This also has the benefit of establishing whether Edith is part of a prominent upper-class family, or another (probably less prestigious) family that happens to have the same name, which would have a bearing on how you treated her. Of course she might be from another prestigious Crawley family somewhere else, in which case Edith might reply "No, of the Wiltshire Crawleys".

I do not know enough upper-class people to know if this was actually done in real life or is merely a trope of fiction, although it was intended seriously in most of the fiction where I have encountered it. These days it is either used ironically or to indicate the speakers snobbishness (because by asking the question they betray their own fixation on whether other the person is related to an important family or not).

In the example you cite it is of course being used sarcastically. Folini is not a traditional British name, and so it is unlikely that there is a prominent upper-class family in Wiltshire with the name Folini. Although in these days of world travel who knows.