Of course it's not free. It's about who takes care of the costs. You should not see a bill from the hospital as your health care provider should fully take care of this.
Story time: When I was a little kid, I stumbled with a glass jar in my hand, fell into the shards and cut my right hand open. Half a centimeter more and I'd have lost three fingers of my right hand completly. Tendons and nerves were cut and the fingers were immobilized immediately.
Never did anyone worry about what it might cost to fix this. Not my family, not the hospital, possibly not even the health care insurance provider.
Instead I was taken to the best hospital for this kind of damage and several high trained professionals operated for 8 hours to fix it. After my hospital time I got movement therapy to get my hand fully working again.
This is a real indicator for a developed, first-world state: Whatever happens to you, professionals will take of you and you won't have to worry whether your family will go bankrupt because you stumbled as a kid or not. Because the society as a whole has build a net that will catch you when things like this happen.