I only had to take two science courses, all the other breadth requirements I'd satisfied with high AP and SAT scores. I still took a language for fun, but I didn't need to. Also, I was responding to someone in Ireland, where those breadth requirements don't exist at university level. I'm not sure exactly which point you're trying to make - you say at first that a student should talk to their professor at the outset to say they're sensitive to a given topic, and then later that bringing it up is rude or attention-seeking. If I'm taking an introductory class, and the name of the class is a time period (British Literature from 1880-1970, for instance) I may expect to see certain works, being familiar with the period, or I may see on the syllabus a work I've never come across. Usually a professor will describe a work at the end of the lecture before you read it, to point out certain things to pay attention to, and I think at that moment it would be worth pointing out whether there is graphic material. That would prompt someone with potential triggers in that material to come talk to the professor privately, and either ask to skip that particular chapter or read an alternative work by that author or similar (usually professors have several other works they wish they had time to teach that they can suggest quickly anyway). That way there's at least a heads up, and an individual looking out for his or her own mental health doesn't have to share personal triggers unnecessarily, or in a way you might see as attention-seeking. I see it as something that can be handled sensitively but casually. For your needle story, it doesn't seem unreasonable that a more sensitive professor might have stated before watching the video that there would be needles, and allow you to excuse yourself before causing a bigger distraction for the rest of the class (passing out and needing to be carried out on a stretcher). I'm not saying it's the teacher's fault, but the teacher knows what you're watching/reading/whatever, and you don't, so it doesn't seem like a terrible idea for the teacher to be the one to say hey, there's a gory part about 5 minutes in, close your eyes or leave and come back in 10 minutes. It's more of a courtesy than anything else, and helps the class run smoothly. I took a history class that covered WWI, and the day we talked about chemical warfare, the professor warned us that there would be graphic photos before he clicked over to that slide. He's not going to avoid showing them, but it's fair to give warning to allow those who know they'd be triggered to take care of themselves. I don't see how he would gain anything by trying to surprise us with them, so why not? How long does it take to say "The next slide will have graphic photos"? It's not a disruption, and might help avoid a disruption. right?
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.