As others have said, it's quite usual here for someone else to call an ambulance and for you to foot part of the bill.
I had a severe panic attack at a train station three years ago. As I was incapable of communicating what was wrong, and was curled up on the floor, a train station employee called an ambulance.
The ambulance staff managed to get out of me that I'd been heading for an outpatient session at the psychiatric hospital, took me there, and I was hospitalised for a weekend because my doctor wasn't on duty and the on call doctor wasn't willing to let me go home without her say so.
Thankfully, I had a low franchise and had already met both that and the upper limit of the deductible... but I was still sent a bill for half of the ambulance ride's cost.
Rather an expensive panic attack.... but I can understand why they called an ambulance and am thankful for the four or five people who helped me instead of just ignoring the shaking woman standing frozen half-way up the stairs.
As others have said, even if you had health insurance if you had not met your franchise you will be eligible for the full cost. If you had met your franchise but not paid over CHF 700 in the 10% contribution you make to bills after you've paid off your franchise you will be eligible for 10% plus half the cost. If you had the bad luck to be so ill during five months that you'd paid out all your franchise AND over CHF 700 10% contributions... you'd STILL have to pay half the cost.
Check what your franchise was. Pay the bill, but send it to your medical insurer here in Switzerland anyway. They should then get back to you with a refund, if you are entitled to one.
(I think the above procedure may vary from insurance company to insurance company... perhaps if you post your insurer someone will be able to give you detailed advice for your provider).
I appreciate it is hard coming from the UK system where we don't have to worry about such things... in my humble opinion, we have better care in Switzerland, but we do pay for it.
If it's going to be a real hardship paying the sum all in one go, I suggest you contact the hospital and ask if you can pay by instalments. I paid off an unexpected medical bill over 6 months because I couldn't afford to pay it all at once. I'm sure the hospital would rather you pay little by little than not at all.