Did Obama Falsely Claim Involvement in Columbia Students' 1980's Anti-Apartheid Divestment Movement?

Former Democratic President (and possible 2020 Democratic Party Vice-Presidential Nominee?) Barack Obama (who's now a Multi-Millionaire) apparently once claimed that he was "deeply involved" in the Columbia University students' anti-apartheid divestment movement during the 1980's. Yet according to David Garrow's 2017 Rising Star: The Making of Barack Obama book:

"Obama would dramatically exaggerate his involvement in Columbia's divestment activism on several occasions, telling one interview that `I was a leader on the issues both at Occidental and at Columbia.' Talking about his two years there to a second questioner, Obama asserted that `while I was on campus, I was very active in a number of student movements,' and particularly `I was very active in the divestment movement on campus.' Several years later, on his first visit to South Africa, Obama declared that `I became deeply involved with the divestment movement,' and `i remember meeting with a group of ANC leaders' or at least `ANC members one day in New York City.' There are no contemporary records or other participants' memories that attest to any such encounter..."

During the 1980's in New York City, though, Obama did befriend Genevieve Cook--whose father was the Director General of Australia's Office of National Assessments [ONA], the country's top intelligence agency, between 1981 and 1989 and an Australian ambassador to the United States after 1989 for a few years (including the year that Australian troops joined U.S. troops in attacking Iraq in the 1991 "Kuwaitigate"/Gulf War) As David Garrow noted in the same 2017 book:

"...Sometime prior to New Year's Eve [in late December of 1983], his [Obama's] friend Andy Roth invited him to a party that Andy's brother was hosting on their 6th-floor apartment at 240 East 13th Street. Jon worked at Chanticleer Press...and other invitees included Genevieve Cook, a 25-year-old...who had worked at Chanticleer...She was born in 1958 to parents who were Australian: Helen Ibbitson, the daughter of a Melbourne banker, and Michael J. Cook, a conservative diplomat who would go on to head up Australia's top intelligence agency before serving 4 years as ambassador to the United States. Her parents had divorced when Genevieve was 10-years old, and Helen then married Philip C. Jessup Jr. an American lawyer and executive living in Jakarta during the 1970's...While she was at Swarthmore, her mother and stepfather Phil had moved from Jakarta to New York, and by late 1983 Genevieve was temporarily living in their spacious apartment on Park Avenue just below 90th Street...

"At the Roth brothers' party, Genevieve...and Obama struck up a conversation that lasted several hours after they discovered their mutual ties to Indonesia and expatriate similarities..."

1981-1989 Director-General of Australia's ONA Michael J. Cook