It's actually worse than that. Each employer has the ability to enter a start and finish date of employment and submit that to the tax office. So lets say your example was reversed where the person was working the first 6 months and then fired but the employer put the entire financial year as the employment period. Then the debt matching assumes that the ATO data is 100% correct and all the other Centrelink data is incorrect (i.e. letter of termination, etc) and you owe everything you have been paid since termination since you were obviously still working and Centrelink employees were too stupid to work that out.
The second part is people studying, since you only have one set of dates to pass to the ATO someone who works at a supermarket at night on and off for a financial year will be flagged at getting a constant amount due to the fact that the ATO data is 100% correct and we shouldn't pay you while you said you were 'studying' so pay it back (and working around Christmas, Easter, etc when there is a lot of cash involved can certainly make it interesting).
Biting the hand that feeds IT
