The company says Sam Altman had not been told Medicare data had been accessed by the agent during June training when he met with Richard Marles in Silicon Valley on September 1 about evolving artificial intelligence capability.
The tech titan found out about the break-in in August, but left Canberra in the dark until it sent an email to a rarely-monitored inbox on September 10.
Mr Altman spoke with Prime Minister Anthony Albanese on September 24 informing him of the breach.
OpenAI's chief strategy officer Jason Kwon faced a grilling from a parliamentary committee about how his team handled the breach, and why Australia was not informed until months after it occurred.
"The process by which people became aware of this incident inside our company could have been much better, and we want to make sure that something like that does not happen again," Mr Kwon said.
"We wanted to understand more of the facts before we spoke to the impacted parties.
"I think we have learned our lesson that it is better, even with partial information, to let parties know that something has occurred, and to also make sure that we're going through all the right channels."
On Friday, it informed the government of another break-in, to a NSW parks and wildlife website in June, with Mr Kwon pledging to more diligently keep authorities in the loop.
Mr Kwon could not confirm to the inquiry whether the agents could autonomously hack into and control high-security infrastructure, like a gas plant.
"It's going to depend on the safeguards and the infrastructure and the security controls that that particular company or provider has in place," he said.
The tech giant will inject independent expertise into its own Australia-based task force on AI safety which is expected to wrap up by the end of 2026.
The federal government has maintained that OpenAI is working closely with it to rectify issues, but the $US850 billion company has been criticised by politicians across the board.
The company also came under fire for its use of artists' content to train AI models.
Independent senator David Pocock blasted OpenAI for refusing to enter into copyright deals with creative agencies, instead requesting workarounds for legal protections.
"We are not asking Australia to do anything specifically for consideration," OpenAI's head of economic policy Adam Cohen said, insisting most creative-based training was happening in the US.
Representatives of artists, musicians, authors and journalists, including the ABC, earlier told the inquiry AI scraping without compensation posed an existential threat to creatives' livelihoods, calling the companies thieves.
The start of OpenAI's appearance was plagued, somewhat ironically, with technology issues. Company representatives dialling in online struggled to hear people in the room.
It came after a morning grilling for its competition, Claude owner Anthropic, which said it would have informed the government of breaches within days, not months.
"As soon as we detect anything of that nature, we would definitely reach out within a matter of days or sooner," Anthropic's head of safeguards Dave Orr told the committee.
But Australian laws lacked the teeth to get AI companies to own up to their mistakes, committee members heard.
"Right now this is largely voluntary, and we're still learning technology and learning how to conduct investigations," Anthropic special envoy and former US ambassador to Australia Jeff Bleich told the committee.
The firm's Australia and New Zealand policy chief David Masters said there were transparency requirements in some laws.
"We would welcome similar laws here in Australia," he said.
Anthropic flagged AI's rise could hurt demand for human workers in its submission to the inquiry, but said early evidence showed the technology would augment rather than replace manpower.
Microsoft's top minds, including general manager Amanda Craig, are next to face the inquiry before Google is questioned on Wednesday afternoon.
