Hi
I had some experiences with swiss authorities, specifically swiss Police.

I have learned that, DO NOT tell them the whole truth, even if they know it sounds fishy. If you tell them the whole truth, they actually will go by the book and "penalise" you, even if you thought by being truthful counts for something.
NO they don't appreciate that!

But tell them some part of the truth, without making yourself a liar, and they usually will accept it.
However do not make things up.

Hope it helps.

HAT