I have no opinion as to what happened when the two were alone, but a jury, if the case went to trial, would be called upon to make a decision based on the perceived truthfulness of the complainant.
I don't quite know what to make of the Daily Mall article and its photos. Graduation at Columbia is a ceremony that dates back to the 1700s! The university is composed of numerous colleges (three undergraduate schools, including Barnard, plus an engineering school, a business school, a medical school, a school of journalism and a large grad school of Arts & Sciences). All of which amounts to THOUSANDS of graduates each May.
Add four guests per grad and there is no space on campus big enough to hold the multitudes. The ceremony is held outside in the sizable university quad (one of the most beautiful spots in NYC, BTW). The class from each school marches in en masse, arranged in alphabetical order, and takes its seat; then the next school's grads come in, etc.
There is (or was when I was there) no parade of grads across the stage and no handing out of diplomas. Instead, the graduation was a mass event and diplomas were handed out in each school's administration office after the ceremony.
So I'm not sure what pictures we are seeing. Perhaps the young woman's school had a private ceremony to hand out the actual diplomas. (Mine had a sort of reception, very informal, and you went up to a desk to get your scroll.)
All of this goes to say I am suspicious of the DAILY MALL's account of the event. I think it's at least possible the mattress was dragged up on stage after the ceremony (notice the podium is empty) for a photo op.
No, according to NYT she brought it on the stage during graduation ceremony. Regular, not a private one.