Thanks oliver2002 and airoli for the responses.
I am afraid it leaves more questions than answers for me, as I am not very knowledgeable on the intricacies of POS and fare construction.

So, basically, ITA shows US POS data? But if I want to fly LX from Europe, shouldn't they have just one fare, in the currency of the departing country? (CHF or EUR)
Why would there even be phantom results from the US POS if the flight doesn't even depart from the US? And where are these phantom results coming from? The LX reservation system or another source?

It also doesn't explain why the LX call center told me the flight was sold out, but swiss.com was still willing to sell me seats...(I was on the computer while on the phone, so it was really a simultaneous request)

So many questions, I know!!
But quite an intriguing topic, I must say...