When the problem is due to deeply embedded causes, you ain't gonna fix it any time soon, and most definitely not "immediately." The govt depts' concern isn't for the harm they've caused this woman, or anyone else. It's simple annoyance at their carelessness being exposed to public scrutiny.
Without knowing a thing about the details, it's still easy to guess some of the systemic contributing factors:
1. Managers with authority but no (or little, or obsolete) technical expertise making decisions they are unqualified to make.
2. Outsourcing development instead of developing in-house.
3. Hiring poorly paid, inept code monkeys instead of facing the fact that truly competent IT people are in very short supply and if you want good ones (not necessarily "the best') you have to pay for them. No such thing as bargain basement experts.
4. The MBA mentality that views employees as fungible assets, all interchangeable cogs, instead of recognizing that every employee has a unique combination of smarts, education, experience, and overall competency. No, dears, that secretary over there is NOT qualified to carry out that statistical analysis you want, even if she has a vague idea what a spreadsheet is.
5. Deadwood in the upper ranks of management who yearn for the days when they had paper records, preferably maintained by hand in blue-black ink with fountain pens.
6. Blairite fascination with big projects, instead of the little dull boring unexciting ones that actually do the hard work.