The needle example is an interesting one. I think if a student declared that they had a phobia of x at some point, I would absolutely warn them that x will be shown in class/present in a text on a particular week. But it's difficult to account for all phobias. What if there was a movie with a spider in it? Or a book? Should the professor warn people with arachnophobia to leave/shut their eyes at a particular point, or skip a particular chapter of the book? _refugee_ mentioned being warned about death being discussed in a text. I've seen course syllabi where every single week could be marked with "Trigger warning: death". It's really difficult to predict how people will react to certain texts, and trying to put in trigger warnings can quickly become a strange guessing game of figuring out (and sometimes spoiling) challenging aspects of texts.
I think it just depends on the context, and the type of class. Like I said, in my mind, it's just a courtesy, not something I would suggest mandating. Now that that professor has had the experience of a student fainting in class, he or she might consider mentioning it in the future before showing the video. I'm not suggesting that we all have to be mindreaders, or that everyone always has to announce to strangers and acquaintances all the things that might trigger them. I guess I'm just saying that there are better ways of addressing this particular type of experience outside of either "it's your problem, shut up and deal with it" or "everyone has to walk on eggshells and cater to every issue". I think those responses are simplistic and immature, and it's not absurd to look for understanding somewhere in the middle.