As someone who has worked for a Swiss company for over 20 years, alongside hundreds of Swiss colleagues, I can categorically declare that statement complete nonsense. Regardless of which of the nation's three official languages is their 'first' (they pretty much all speak all three - and English...
All?
Like (off the top of my head) England's Jamaica-born Raheem Sterling? Germany's Polish-born Lukas Podolski and Miroslav Klose? Ghana's German-born Kevin Prince Boateng? etc, etc, etc?