Unless you have insurance coverage which reduces the excess to zero (this is not standard, it costs quite a lot extra), then you will have to pay anything up to the excess.

Rental car companies are used to people doing this - despite having stickers on the fuel filler flap and often on the fuel gauge and the key fob. When it happens, as you long as you do not pull the fuel into the engine, ie by driving the car, all that is needed is to drain the fuel tank, refill and all should be OK. You will not get that done, including a VAT charge for CHF300, so I think the initial info you were given was rather optimistic. The breakdown of costs sounds to me much more like what Hertz would incur, plus the fees that they add on for things like this.

I would not hold out much hope that that total will get reduced.