The Ministry of Health recognise that Audiologists and Audiometrists who are Members of the New Zealand Audiological Society (NZAS) are qualified to fit hearing aids- that’s why the Ministry of Health funding schemes are only available to Members of the NZAS.  Look for someone with the qualifications MNZAS or NZAS Audiometrist.
The ACC and Veterans’ Affairs only provide hearing aid funding if an Audiologist Member of the NZAS is solely responsible for testing your hearing and fitting your hearing aids.  This requirement appears to recognise the higher level of training of Audiologists compared to Audiometrists.