They were also asked to go for psychiatric testing with a state-sanctioned professional before any compensation would be paid, News Corp Australia reported.
"No family should have to suffer the passing of their baby and then be put through unreasonable legal hoops," Hazzard's spokeswoman said.
The minister spoke to the family solicitor and has offered to meet the parents.
Another baby, Amelia Khan, was left with permanent brain damage in a similar mix-up at the same hospital in June 2016.
The Khans hired lawyers last year to handle their compensation claim.
"We are assisting the Khan family in working cooperatively with the state Government and their lawyers to ensure Amelia gets the best care and treatment," Maurice Blackburn lawyer Libby Brookes said.
Opposition health spokesman Walt Secord has sought an assurance from Hazzard that both families are being treated fairly, appropriately and sensitively.
"This is not a backyard legal dispute, this involves the death of a baby and baby who is going to be permanently affected for the rest of their life," Secord said.
"The Government's handling of this has been extremely disappointing. I think they've treated both families unfairly."
The hospital's general manager and acting director were both stood down and an investigation was carried out into both incidents.
A report released in August 2016 pointed to "a series of tragic errors" at the hospital including incorrect installations of gas pipelines, flawed testing and significant clinical and management failures.
Then Health Minister Jillian Skinner faced criticism over her handling of the gas scandal before she was dumped from Cabinet when Gladys Berejiklian took over as Premier in January.
- AAP