> If you pay them even a tiny amount each month the bill never goes to a collection agency, which means it never hurts your credit score.

This doesn't follow - I am pretty sure that institutions can report things without a collection agency being involved. Which isn't to say it might not be a good strategy nonetheless - an institution like a hospital might be less inclined to report things if they are still receiving checks from you, whereas I don't see a collection agency giving the same leniency.

Overdue medical bills (specifically medical bills) do not affect your credit score, and are never reported.

Unpaid ones are reported sometimes, but not overdue ones.

This is because a medical event is not considered as your fault, so if you can't pay it it's not because you are a poor credit risk for other things.

> Unpaid ones are reported sometimes, but not overdue ones.

What is this distinction?

Unpaid bills go to collection agencies, overdue ones (i.e. still being paid, but not in full) are left in house.

Medical providers don't report to credit bureaus, but collection agencies do.