This part stands out to me:

    EN> They base their accusation on the fact that she also gives online language courses to Americans and wants to meet some of her students for coffee in New York.

To me, that is good police work. I see it quite a lot when I am travelling: People (visibly foreign) giving language lessons by video chat or phone call. Obviously, they don't have a work visa to do it, nor will they be paying local taxes on those wages. I have even asked people about it. Each time, they casually reply: "Yeah, I always work a little when I travel to make more money." The shock never wears off for me -- that people can casually break the law in a foreign country when it is convenient for them. It would have been better for that (Swiss?) person to apply for a regular tourist visa at the US embassy in Switzerland, make clear her job and her intention not to work while on holiday. She made too many assumptions when using the ESTA. There are so many stories online about people writing dumb things on social media then experiencing "friction" at the US border. The ESTA application even specifically warns about it. Again, my sympathy is low.