Did Hillary Clinton fudge a detail in her LSAT recollection?

Some critics are raising questions about Hillary Clinton’s recollection of a negative experience before she took the Law School Admission Test.
Clinton wrote at the Humans of New York blog that she was one of only a few women waiting to take the test when men in the exam room began harassing the women. The men said the women shouldn’t be taking the test. According to Clinton, one man even said that if she took his spot in law school, he would get drafted and have to go to Vietnam.
Critics point out that, at the time Clinton took the test, a new law had eliminated draft deferments for those attending graduate school, the Washington Post reports. But it’s not that simple, the article says.
Clinton has said she took the LSAT during her senior year at Wellesley College, which means she would have taken the test in the fall of 1968 or the spring of 1969. A 1967 law eliminated mass graduate school deferments, and President Johnson announced he would implement the law for the 1968-69 school year for all but medical, dental and divinity students. Everyone else in grad school would be subject to the draft.
But “the draft was in flux in 1968,” the article says. Then-presidential candidate Richard Nixon said he would change the system, possibly by implementing a lottery. Local draft boards had a lot of independence and there was a lot of flexibility in the system, according to University of New Mexico law professor Joshua Kastenberg. A “de facto deferment” still applied to graduate students, who could attain hardship deferments, he said.
“Graduate school still acted as a shield,” Kastenberg told the Post. “It was very clear that after 1968 graduate students still had significantly less chance of being called up.”
Among those who received deferments were Bill Clinton (who pledged to join ROTC then gave it up when he got a high lottery number) and Rudy Giuliani (who sought an occupational deferment while clerking for a federal judge).
Hillary Clinton told her story about a bad LSAT experience as early as 1996 in a New Yorker interview, though it didn’t include the Vietnam war reference. She told the story again in interviews in 2014 and 2016, with the draft reference.