With an high deductible plan, which many have, or for those with less money to afford good insurance, they very well COULD be stuck with a bill like that, or a large portion of it.
For a broken arm. I think we had a lower bill for my kid's childbirth costs.
Child birth costs some friends paid for their kid: ~$60
Child birth costs I paid for my kid (poor insurance plan): ~$3300
I think that the total bill for the child birth (in my instance) was around $18K. I'll note that if you were uninsured, that would probably be significantly more. That $18K cost is negotiated between the hospital and the health plan I had at the time.
For a broken arm. I think we had a lower bill for my kid's childbirth costs.