Either you or her has got the wrong end of the stick here. Housing insurance is a compulsory part of any loan a bank will give and therefore solely the responsibility of the renter. Contents insurance is entirely up to you whether you want to pay the rate or not but I would say you will be broke if there is a fire and it is your fault - think about the value of your clothes rather than ikea "sticks".

What you will often need, though, before signing a rental agreement is personal liability cover (Haftpflichtversicherung). It is rare that they check but I did have to provide this once. The cost is around the SFr. 100 and covers you for multiple millions of damage you might cause.