Longtime lurker, first time poster. I thought I'd shed some light on this situation based on my somewhat educated opinion on how the "invasion of one's privacy" is a legally malleable concept. I think most posters are spot-on in that when one acts in the presence of 6 others in a room, that action does not come with an expectation of privacy to those six people. However, one does not inherently consent to the release and dissemination of a video of that act (especially a sexual one) to others outside of the room (via a snapchat video or otherwise). In other words, there's an argument available to anyone who was present for the alleged sexual encounter to say, "Yes, I consented to all the actions in the room. Yes, I consented to being video taped. But, I did not consent to publishing the video on social media and acts deemed private among those in the room and made available on video on social media. Therefore, my privacy [as I reasonably expected it to be to those outside of the room] was invaded." That's what I believe the crux of this situation is.
Further, even if the video was removed from social media or the internet, there are rules of evidence that will allow for the recovery of the meta-data/ account activity history of anyone who is alleged to have posted the video on the internet/ social media app. They can use this information to put some of the pieces to the puzzle as to when this could have been possibly posted together.
As to the "inconsistent statements" argument, there's some shaky ground there no doubt. But, the inconsistent statements could be related to the sexual assault issue and not necessarily the invasion of privacy issue.
Feel free to disagree, but this is my speculation as to why the one who allegedly videotaped and posted this video could be in hot water...