One went to the Health and Disability Commissioner, after being declined a C-section in June.
They were encouraged to clarify her rights with the DHB, a spokesperson for the watchdog said, and the HDC "alerted the DHB to the consumer's concerns".
"HDC's role is to resolve complaints about health and disability services provided to consumers. We are not able to compel a provider to provide a service if there is no clinical indication to do so," the spokesperson said.
"We also acknowledge DHBs operate with limited funding and as such are obliged to prioritise the services they offer to consumers."
Auckland DHB chief executive Ailsa Claire said the HDC complaint wasn't upheld, "as the response stated that the Health and Disability Commissioner cannot compel a DHB to provide services where there is no clinical indication".
Another two complaints were received by the DHB, from patients whose private obstetricians asked for them to have an elective caesarean section.
"Access was declined as there was no clinical reason stated. These obstetricians were asked to provide additional information regarding the clinical indication for the C-section, and once this clinical need was established, these C-sections went ahead," Claire said.
The tension surrounding C-section requests and private obstetrician access was revealed by the Weekend Herald yesterday.
For "low risk" women giving birth for the first time at the hospital in 2019, the C-section rate for those using private obstetricians was more than 50 per cent, compared to a national average of about 21 per cent.
There is a lack of private birthing facilities, and for decades women looked after by private obstetricians have used Auckland DHB labour and birthing facilities, under "access agreements" with individual specialists.
No new access agreements for private obstetricians have been granted for more than 12 months, with Claire saying the "pause" on providing access to any more private obstetricians would remain throughout engagement with groups including specialists, midwives and patients.
The issue was discussed at the most recent DHB board meeting, with minutes noting, "while women have the right to determine where to have a primary birth they do not have the right to determine whether they can have a C-section or induction; this should be decided on the basis only of clinical need".
"For historical reasons Auckland DHB is the only provider across the region that offers access agreements to private obstetricians which is why there is a high proportion of non-domiciled [women living outside the DHB boundaries] women coming to Auckland DHB for private birthcare."
Auckland DHB board chairman Pat Snedden noted any move to change that situation "would cause contention within the marketplace and perhaps some alarm". In response, Claire said the argument was "about quality of care and fairness".
"Women who choose to have a private care package pay their clinician privately a fee agreed between them but they do not pay Auckland DHB for the privilege of accessing private care," the board minutes summarised.
"The issue is that these women are receiving high-cost healthcare when there is no clinical reason for it.
"The DHB has limited resources and Auckland DHB provides the majority of services to people who cannot afford a private obstetrician. That means when the private obstetrician comes in and uses theatre capacity that theatre becomes unavailable to the rest of the Auckland population."
Chief Medical Officer Dr Margaret Wilsher noted, "Intervention rates are inexplicably high for private obstetricians and that is extremely worrying given the morbidity rate that is associated with these interventions. The data simply speaks for itself."
Private obstetrician practices approached by the Herald on Sunday declined to comment, one citing legal advice.