I'm not sure where you draw the line for this, but last time I went into Switzerland I had my passport checked at the border.

  That's because Switzerland isn't part of the Schengen area

(https://en.wikipedia.org/wiki/Schengen_Area)

So if you fly in from the UK (or any non-Schengen country) you need t show a passport. As is the case in any other Schengen country.

https://en.wikipedia.org/wiki/Schengen_Area

And random checks at the border are permitted (i.e. contraband, people trafficking).

Also a country is allowed to re-implement border controls in case of crisis.

And how exactly do you show that you're a citizen of a country in the Schengen area without showing a passport?

I think that's the case in most Schengen airports now.

What can happen is that you're checked by customs at the border. Since Switzerland is not in a customs union with the EU. Generally speaking, though, it's free flowing.