This is not right! Why should I pay a debt due to someone else's mistakes?

I was issued with this debt after arriving to my parents for Christmas holidays. I was embarking on a 6wk holiday. I was still keeping up with the costs of my living while I was away - rent, power bills etc. I also had Christmas to deal with. Prior to my holiday, my bank accounts were hacked and majority of my money was stolen.
This debt is apparently from 5years ago.
After initial contact with Centrelink, I requested an explanation via phone call. When I received this call, I was passed off to the debt collection department where I was informed that i was not eligible for a payment plan. I was in fact required to repay the debt immediately. After explaining my current situation, I was shown no empathy and informed that if I didn't make payment, my wages would be garnished and if I chose to fight this that I would be taken to court, where I would not stand to win and that I would go to jail. Taken from my daughter until the money was repaid. I was then informed that if I could prove these figures to be incorrect, that any payment would be reimbursed to me. It was then explained to me that according to my file, it was evident that my efforts to report my earnings per fortnight were on track and that the reason I had to update my income assessment could be due to someone entering my report of earnings into the system incorrectly. Why should I pay a debt due to someone else's mistakes? This issue has weighed heavily on my mind. Caused much distress and turmoil during the Christmas period. I was not able to provide my daughter with the Christmas she deserves due to unnecessary concern over this debt.