Appearing before a public hearing on Wednesday, the university's vice-chancellor Genevieve Bell also confirmed students accused of displaying the Nazi salute and Hitler moustache online had no adverse findings made against them following an investigation.
She said the "thorough" probe found those reported incidents had not happened.
Professor Bell said a female student who went on ABC radio calling for people to back Hamas, which launched the deadly October 7 attack on Israel, had her expulsion following a disciplinary process overturned on appeal.
Genevieve Bell said the ANU seeks to balance academic and speech freedom with psychological harm. (Lukas Coch/AAP PHOTOS)
"Do I wish that she hadn't said that? Indeed," the vice-chancellor said.
"One of the things that I think demands constant clarity and attention is what is actually capable under the banner of free speech and academic freedom, and I think that's the thing we need to constantly test."
In response, Labor MP Josh Burns - who is Jewish - said he found "that answer absolutely remarkable".
Prof Bell said the university sought to balance academic freedom and freedom of speech with psychological harm.
Vice-chancellors from the University of Sydney, the Australian National University, the University of Queensland and Western Sydney University, alongside members of the student and educators' unions fronted the inquiry into anti-Semitism on campuses.
University of Sydney vice-chancellor Mark Scott said he acknowledged the institution "did not get everything right in our response to the events on our campus following the October 7 attacks on Israel".
He said the university was doing work to provide a civic campus program to train young people to have respectful debates and discussions with others holding differing views.
With university students set to return in a matter of weeks, the institutions have acknowledged an increase in anti-Semitism and committed to prevent its occurrence on campus with education and disclosure initiatives.
"We support freedom of speech but draw the line at hate speech," Western Sydney University's submission said.
"Our campuses are no place for anti-Semitism, Islamophobia, racism, hate speech, intimidation, or violence."
The spotlight has shifted from higher education institutions to broader Australian society after a string of anti-Semitic attacks in Sydney and Melbourne.
Cars have been set alight, a synagogue burnt down, anti-Semitic slurs painted on buildings and cars, and on Tuesday, a childcare centre close to a place of worship was set ablaze after hateful graffiti was sprayed onto its walls.
Prime Minister Anthony Albanese visited the Only About Children centre in Sydney's east and decried the incident as a "despicable and horrifying crime" before bowing to pressure and convening a national cabinet meeting to address attacks aimed at the Jewish community.
The nation's leaders agreed to establish a national database to track anti-Semitic incidents and reaffirmed their commitment to stamping out the hate crimes.
The Australian Federal Police are investigating whether overseas actors paid locals to carry out the anti-Semitic incidents.
