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Deanna Trevarthen died in December 2016 from mesothelioma, a lung cancer caused by breathing in fibres of the material, previously used widely in the construction industry. She was 45.
Ms Trevarthen said she had been exposed to asbestos as a child, while her father was working as an electrician - an occupation that at the time had high exposure to asbestos.
Between the ages of four and 10, she would hug her father when he was wearing his work clothes and would also sometimes play at his work sites.
Before her death, she pushed to get ACC cover for financial assistance, but was rejected because she was not exposed to asbestos at work.
But the Court of Appeal, in a unanimous decision, confirmed that non work-related mesothelioma such as Trevarthen's was a personal injury for which ACC cover was available.
Dismissing the ACC's case, the Court of Appeal ruled that the exclusion provision of the Accident Compensation Act 2001, which states cover is not available for personal injuries caused wholly or substantially by a disease, did not apply.
It found the operative cause of the personal injury was an accident - the inhalation of asbestos fibres. It ruled that ACC's argument that the disease is what caused the personal injury drew an artificial distinction between a disease and its physical manifestations.
Trevarthen's claim for cover had been declined by ACC on January 11 in 2016 because of its gradual onset, which ACC stated showed her mesothelioma was not a personal injury caused by a specific accident on a specific occasion.
Rather, it argued, it was a gradual process disease that had not arisen from work exposure.
Trevarthen had requested ACC to reconsider her claim for cover on the basis that the disease had arisen from the inhalation of a foreign object on a specific occasion.
The review accepted that mesothelioma caused by asbestos inhalation would meet the statutory definition of personal injury, rejecting ACC's argument that the exclusion of personal injuries caused wholly or substantially by a gradual process, disease or infection applied.
"If the evidence establishes that the mesothelioma was caused by the inhalation of asbestos fibres then the mesothelioma must be viewed as a personal injury, in and of itself.
"The cause of the mesothelioma would then not be due to an idiopathic disease, but rather due to an external, non-disease related agent," the review decision stated.