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

That's wrong. Since 2008 Switzerland is definitely part of the Schengen area. While the UK is not.

(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.

Thanks for the hint, I rechecked and you are right, that part of my comment is outdated. The other part (about immigration) is current.

"All four European Free Trade Association (EFTA) member states – Iceland, Liechtenstein, Norway, and Switzerland – have signed agreements on association with the Schengen Agreement, even though they are outside the EU"

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