As a UK resident, I find that distressing. The idea that needing medical treatment might impoverish me or poverty leaves me unable to obtain the treatment I need seems exceedingly cruel.
We had insurance, although nearly a year later we received a call from the hospital saying that our insurer had refused to pay, and that we'd be responsible for the bill if the insurer didn't come through. The insurance company claimed that the hospital hadn't provided the complete paperwork, and the hospital claimed it had provided the information multiple times.
We received two more calls about it, each about six months apart. It's been a couple of years now, but it still feels like it's hanging out there - that we may get a call at any time claiming that we owe this huge sum of money.
I'll add to that that creditors tend to ignore medical debts (according to a credit analyst I know), and that hospitals tend to cut deals for the under-insured.
Bill collectors can't harass you for medical debts
A Google search lead me to the Illinois State AG's website, which claims bill collectors certainly can attempt to collect medical debts. So your claim might only be true in some states (or none at all...)