The Mother is entitled to an Aged Pension because her home should not be counted as an asset.
This is according to an internal Centrelink document summonsed by her son, DZJ, despite much resistance by both Centrelink and TAG.
An extract is reproduced below which shows the asset exemption if conditions 1, 2, 3 and 4 below are met.
Nobody disputes that 1, 2, 4 are met. However 3 should be applying at this very moment
because the Mother's income (rent) is above the Centrelink specified threshold.

So to parahrase, currently the Mother is in the following erroneous situation because of the DAC.
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Because she pays no DAC her house counts as an asset.
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Because her house counts as an asset, the Centrelink means-test disqualifies her from an Aged Care Pension.
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Because she has no Aged Care Pension, she cannot afford the care fees in the ACF
without selling her house.
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If the house is sold it becomes a huge asset which would eliminate her free accomodation and in fact she would have to pay huge fees instead.
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Also if the house is sold, the son DZJ, who lives there, could not continue his daily care regime for the Mother because the ACF neither has adequate staff nor can they be trusted to not blunder like they have in the past.