Does recording video of a scientific presentation violate the privacy of a PhD student?
EDIT: This post has been restructured into a clear answer, rather than the discussion format it was originally in. Thank you Stella Biderman.



Recording a video of a scientific presentation by itself need not be an invasion of privacy. The invasion comes if and when the video is shared, depending on the nature of sharing medium, the control over shared content and agency to withdraw/clarify one's statement.

A departmental talk may be recorded for internal review. A conference talk may be officially recorded (though I have never seen this personally). As long as these are not shared, and are stored for internal use (quality control, archive, proof of the event), privacy is not invaded. Even so, many individuals may find this distasteful, uncomfortable and even repulsive. This should be respected to the extent possible.
Personal choice is crucial. A conference is certainly a (restricted) public presentation, but presenters go there voluntarily. If someone wants to go on YouTube, that's fine. But nobody is allowed to make them go there. The concern of agency is also important- does the presenter have the right to retract or clarify their stand? Once on social media, it is near-impossible to issue 'errata' or pull something down once people start sharing it.

Yes, video is different from writing.

The medium is of crucial importance, because it determines how the content is disseminated. A journal paper is restricted to subscribers (let's leave illegal downloads out of all discussions).  An open access paper is open to all, but typically accessed by those with a prior interest. Both have restrictions on how it can be further shared and used. This is not the case with videos on social media. Those are seen by a mixed population with different levels of interest. They can be shared very easily and without accountability. They lend themselves to defamatory and potentially abusive comments and unwanted, non-constructive scrutiny.

The nature of delivery determines the audience. YouTube is not an academic medium. Neither is a regular newspaper. Both are good for certain purposes, both may be used for outreach and even educational purposes, but are sub-optimal for sharing research. The packaging of academic content to make it engaging to the general public is a serious and involved matter, which should be handled by dedicated workers with necessary expertise. A typical PhD student is not expected to have this expertise. (After all, how many academics after Feynman do you know who did this on a large scale?)