The Court of Appeal overturned that decision last June.
"We agree with the Court of Appeal that it is not possible to argue that there is no engagement until the second or later period of care occurs nor do we see it as possible to find that carers who provide service with some regularity such as Ms Lowe are engaged, whereas those who provide it on a more intermittent basis are not," Justices O'Regan and Arnold said.
"The key aspect of engagement, being the selection of the person who is to be engaged, is clearly undertaken by the primary carer and the work that is undertaken by the relief carer is undertaken for the primary carer without reference to the ministry or the DHB."
Justice Young agreed for slightly different reasons in that the primary carers engaged the respite carers and that the ministry provided a subsidy.
"On this basis, the 'trade or business' of the ministry does not encompass the provision of respite care and the 'work' carried out by respite carers is not 'for' the ministry," he said.
Chief Justice Sian Elias and Justice Susan Glazebrook formed a different view and would have allowed the appeal because "the ministry and the DHB clearly promise in the claim form to pay if the full-time carer does not," they said in their opinion.
Finally, that it may be inconvenient or expensive to give carers like Ms Lowe the rights to which she is entitled is not a reason to read down the definition of homeworker, they said.