An OpenAI agent infiltrated a Medicare data portal on June 18 in the first known instance of autonomous software breaching an Australian government website.
The break-in made global headlines after Prime Minister Anthony Albanese disclosed it during a visit to the United Nations.
What, if any, action should be taken against the tech giant is being examined by a task force that is expected to report back in a matter of weeks.
OpenAI boss Sam Altman and Anthropic chief executive Dario Amodei may also soon have to answer a Senate committee about the breach.
But legal retribution for wrongfully accessing classified information was "missing the point", deputy opposition leader Jane Hume said.
"I'm not entirely sure who it is that they're going to put in cuffs and drag through the city streets and put in the stocks," the Liberal senator told ABC's Insiders program on Sunday.
"The real alarm bell that was set off this week is the fact that the only reason we knew about this breach ... is because OpenAI told us."Â
Aggressively going after big tech risked repelling AI firms that could also help build the cyber defences Australia desperately needed, Senator Hume said.
She also criticised Prime Minister Anthony Albanese's advocacy for global AI safety standards at the UN General Assembly meeting, putting him at odds with US President Donald Trump's view the technology should go essentially unregulated.
"I don't necessarily think that finger-wagging at our trusted partners or in trying to gazump Donald Trump is the way to go about that," Senator Hume said of the need to partner with US AI companies.
Greens senator Sarah Hanson-Young, who chairs the committee summoning Mr Altman and Mr Amodei, said the two bosses had to prove their concerns about AI safety were genuine.
Both men recently urged governments to work together to contain AI's harms and ensure the technology remained under human control.
Parliamentary probes can only force people in Australia to appear before inquiries, but Senator Hanson-Young argued "it'd be a pretty bad look" for OpenAI and Anthropic to ignore the committee entirely.
The firms could opt to send local representatives, rather than more senior overseas-based executives.
AAP has contacted OpenAI and Anthropic for comment.
But tech giants' relationship with Canberra could still remain friendly even if the government pursued the company vigorously over the Medicare breach, Deputy Prime Minister Richard Marles told News24.
"What has happened here with OpenAI's agents is completely unacceptable and we've made that very plain to Sam Altman," he said.
"But we are grateful for being able to work closely with OpenAI."
Mr Marles revealed he met with Mr Altman earlier in September, after OpenAI discovered the hack during a broader review of its agent but before it notified the government via a public email inbox.
"We didn't speak about the incident and this was before there had been a notification to the Australian government in any form," he said.
"We have raised with OpenAI our concern about the fact we were not notified earlier and indeed in the form in which we were notified."
However, he said was reassured by the US AI company bosses publicly calling for policy guardrails for their own technology.
"I take concern from what occurred last week, but I take heart from their words," Mr Marles said.
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