Actually usually it doesn't. They'll say as an incentive to pay it that it won't go on your credit report.
You can only report past due payments, and outstanding debt. But if you take the offer the debt is not past due. And most non-credit agencies (i.e. those without a regular payment schedule) never report past due in the first place (only unpaid).
I am suggesting that in the new system, a credit ding would come along with the debt reduction.
In fact, elsewhere on this thread, I suggested that perhaps the size of the ding would be proportional to the size of the debt reduction. This gives the debtor more incentive to pay as much as possible.
Perhaps not, if it resulted in a credit ding.