He went on to warn that such allegations can ruin a young man's life: "Don't put yourself in a situation that would cause you to be trying to explain something that really needs no explanation had you not put yourself in that situation."
His unusual address has found an audience on YouTube, and angered some parents and faculty who say the president appears to be blaming women for sexual assault. It came at a time when the federal government is cracking down on campuses across America over their handling of such cases.
Carmina Taylor, president of the Lincoln University Parents Association, said she took calls from concerned parents who had heard about the ceremony from their daughters.
"It's frightening," added the Rev. James Thomas, of Los Angeles, whose son is a junior. "There had to have been at least one young lady in that room who had been the victim of sexual assault who had not reported it, and there was nothing that was said by the president that would have given any comfort."
Marybeth Gasman, a University of Pennsylvania education professor and expert on historically black colleges, called Jennings' remarks "disturbing, offensive, and sexist in nature."
"The president blames young women for being raped by saying that when they have sex with someone and regret the act, they then create a story [of rape] to explain it."
For Jennings, a career educator who has led the 1,819-student college since January 2012, the speech has become yet another point of contention in an embattled tenure and illustrates a leadership style that some critics find too autocratic.
But Jennings, who also was the subject of recent no-confidence votes by both faculty and alumni, said his remarks were taken out of context in the clip, which shows four minutes of his 26-minute talk. He said he was referring to three cases in which women falsely reported rapes as revenge against men who had been unfaithful.
All three cases were investigated by the university and reported to authorities, a university spokesman said.
Michael Noone, first assistant district attorney in Chester County, said he has no reports of rapes at Lincoln from last semester. There was one allegation of attempted sexual assault, but the case was dropped, he said, because it could not be proved beyond a reasonable doubt - not because the woman recanted.
Other sexual-assault allegations have been found since he became president, Jennings said, and the campus took appropriate action. Lincoln declined to provide a number, referring a reporter to the university's 2013 crime report. It showed reports of three rapes, two sexual assaults, one domestic-violence incident, and two dating-violence incidents.
"No one would ever discourage a young woman on this campus from reporting a sexual assault," Jennings said. "In fact, I emphasize to them how serious that allegation is and that the university takes it very seriously and so does the federal government and so does the court."
He said he also addressed the issue at the male convocation: "I made it very clear to the men on campus that no means no."
Not everyone was offended.
"I personally didn't find anything wrong with what he said," said Carla McDuffie, a New Jersey parent. "I found what he said to be true as far as how he characterized males in that particular context of the conversation."
For faculty members, the speech may be the least of their concerns. They cite a 19 percent drop in enrollment since Jennings took over, high turnover in administrative posts, and the elimination of the teacher-education program - a result, Jennings said, of low enrollment.
Last month, two-thirds of the eligible faculty voted on Jennings' leadership, with 58 out of 64 educators expressing no confidence. That followed a no-confidence vote by members of the alumni association in May who were upset that Lincoln's master plan called for demolishing several historic buildings on campus and who opposed Jennings' decision to change the day of commencement without consulting alums.
Seven senior faculty members who helped organize last month's vote spoke with a reporter about their dissatisfaction.
"There's a general feeling of unease that if nothing is done, we could just wake up one morning and [Lincoln] will cease to exist," said John Chikwem, a microbiology and immunology professor for 19 years, whose four children attended Lincoln and whose wife works there.
"It's a feeling of complete instability," added Dana Flint, a philosophy professor in his 35th year.
Kimberly A. Lloyd, chair of Lincoln's board of trustees, said that trustees "will be carefully reviewing the vote and the concerns accompanying it."
Jennings, whose contract runs through December 2016, came to Lincoln, a state-related university, from the South, where he was running a family business. His last university president job, at Alabama A&M, ended in 2008 with the board of trustees terminating his contract over accusations that included paying an executive assistant for two weeks when the assistant was not at work.
When Jennings, who has degrees in sociology and education, arrived at Lincoln, enrollment already was on the decline and finances were tight, conditions faced by other historically black colleges, including nearby Cheyney.
Jennings blamed campus discord on changes he made to erase a deficit he inherited. Students had been allowed to attend without paying tuition. He made them put down 80 percent before they started classes.
"This is a business," he said, "and I run it as a business, because if I don't, we'll be out of business."
Similarly, he changed graduation from a Sunday to a Friday so Lincoln wouldn't have to pay double time to employees.
"Nobody likes change," he said. "But I walked into a situation where a number of things had to be changed."
Such as relations between the sexes.
At Lincoln, more than 50 percent of students come from single-parent households and nearly two-thirds are the first in their families to go to college, Jennings said.
"You find yourself having to parent," he said.
Several female presenters also offered advice during the convocation; one warned against showing panty lines and wearing dark bras under white shirts. The full 46-minute video was taken by an audience member and obtained by The Inquirer.
Jennings said he sought to point out how men can deceive and exploit women and how women have to protect themselves.
"Men treat you, treat women, the way women allow us to treat them. . . . We will use you up if you allow us to use you up," he told students. Then men will "marry the girl with the long dress on."
Parent Sonya Lloyd, of Bowie, Md., said she was so upset by the video that she won't send her 17-year-old daughter to Lincoln.
"I felt like he was pointing the finger at these girls," said Lloyd, whose son is a junior. "If that happened to my daughter, God forbid, are you saying it was her fault?"