Mr Dunn said he noticed Mrs Tregonning standing with the man on the lawn soon after, but did not believe she had saved the man as she claimed.
He said she just stood outside and "barked" orders.
Yesterday, Mrs Tregonning said she stood by her version of events.
By the time she got to Mr Pittaway's door, the flames had taken hold and he was standing in the doorway. She reached in and pulled him out.
The man kept trying to go back inside to find his cat, and people in the area had to stop him.
She never saw Mr Dunn, but details had emerged since the fire that he had arrived before she did.
She did not dispute Mr Dunn's actions.
"When I got there, the man was still standing just inside the door, so perhaps he went back inside after the other guy had taken him out. From what I've heard, it sounds like he's been saved twice."
Mrs Tregonning said it had been a traumatising experience, not withstanding the criticism she had received from people in the "Dunn Camp".
"I've not asked for any of this. It was the neighbours who pointed me out to media and the police.
"If that's the way he sees it, let him have the kudos. It's getting out of hand. I never wanted the kudos.
"The big picture is, it was a community effort. It's not down to one person. The main thing is, [Mr Pittaway] wasn't injured or killed."
Southern Region fire safety officer Barry Gibson said his investigations had revealed Mr Dunn was first on the scene, and he had coaxed Mr Pittaway out on to the deck of the flat.
"I believe he [Mr Pittaway] has tried to go back in. He was still on the balcony when Sarah arrived, and with all the smoke, she may have thought she was reaching through the door to pull him out, but it was actually a trellis near the door.
"Sometimes adrenaline runs and it's not always clear what you've done.
"They both did a good job and their efforts were admirable," he said.
A Dunedin City Council spokeswoman said four tenants were affected by the fire.
Mr Pittaway was treated at Dunedin Hospital for smoke inhalation. He received support from the Patients and Community Trust (PACT), which would rehouse him.
She said the council had insurance and the intention was to rebuild the damaged unit.
The council owns about 960 units in Dunedin. In 15 years, staff estimated there had been about five fires in council units.
