$2,000 is not a "large medical bill" in the US. An unexpected medical problem will likely cost a lot more.
Hospitals have to treat you regardless of your ability to pay.
The whole situation is far from optimal though.
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.
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...)