Ok, just got it translated from German to French and for you, and I now get it! After looking more into the bilateral agreements, I've found out something interesting.

Unfortunately, this is correct.

This is because, in your country, when you were working, part of your wage was going to the governement to pay for your health insurance (like in the UK).

As you are no longer working in your country, you are no longer paying into this system. Therefore, any "dependents" over there are no longer allowed health cover under that system.

You therefore have to cover them for basic here in Switzerland so that they have at least some cover.

This post may be useful for UK residents who fall into the same category as you......