Yes, they do, but apparently only for the toll free Swiss US number.
A woman in Basel said, "officially, Swiss does not have a call center in Fiji".

That is SwissSpeak for "it's true, but I will deny it".

I finally got a human response from Swiss US, "We regret...bla bla" and offer me 5000 flyer miles.

And what are 5000 miles worth? $1.50?

You have to be a genius to cash in miles these days. I quit KLM after 10 years because without warning me, they vaporized 52,000 miles.