Installment Agreement Paid and Still Sent to Collections By Utility Company

I moved to NC from NYC and had to close my account with my gas company, National Grid/Keyspan. Since I'd been on Balanced Billing to help manage my payments monthly (which I also paid as agreed each month) I was immediately set up with an agreement to pay the remaining balance of $571. I made a downpayment and an agreement was drafted that I would pay $100 a month for 5 months until the account's balance was $0.

Upon checking my recent credit report, I noticed that the account was listed as a Collections account. However, I have been paying every month as agreed. After calling the utility company, they explained that regardless of whether the consumers pay the balance or not, as soon as an account is closed it automatically goes to collections. They claim that as soon as I make the last payment, the balance will be shown as satisfied and, though it won't be deleted from my report, will turn into a "positive" item on my report and will no longer be listed as negative. Doesn't really make sense to me, though.

Is this item negatively affecting my credit score? Is there any use in even shelling out the rest of the $200 that I owe at this point if it's going to be listed as negative (paid in full) anyway? I've always paid everything on time and this is the only item listed as "potentially negative" on my report. I really feel as if it's not fair for me to be punished for paying an agreement they set up for me each month on time (as I couldn't pay all of that at one time, obviously) only for them to immediately report me as if I never paid anything as soon as I was forced to close my account. I feel cheated and mislead into paying.