ERA member James Crichton said it had made an error, "which it regretted", by issuing its finding before the Learmonths had filed all their submissions.
The ERA found Mrs Learmonth had taken Ms Akeson to the airport in Samoa, arranged her flight home, stayed with her for up to an hour and left her with $90.
"The authority must again vacate its original conclusion ... and substitute it with a fresh conclusion that, whatever happened when Ms Akeson commenced to leave Samoa for New Zealand, no criticism can be levelled at the Learmonths, based on the evidence now before the authority," the decision said.
Mrs Learmonth said she was "over the moon" with the result.