It is more or less a scam that is based on your parking offence
. They are trying same things from Croatia.
- if they want to take things further they need to do them in Swiss court
- if they do this they need to prove:
the merits of the case (that you didn't pay)
your guilt, photo that you got is not a proof.
It is going to be a civil case not one for traffic offence, so it is not automatically responsibility of the owner of a car. They have to prove it was you who parked the car.