I do feel bad for the intern, but that's what happens when people think the internet is like goofing around with their friends, not a public space where everything you wrote could potentially be read by everyone forever..
Most people would not behave like this if they were interviewed by their local TV news crew, but somehow, it's different because it's the internet.
I'm not a law expert or anything like that, but as far as I understand it, personally identifiable information could potentially also apply to public comments or posts that contain personal information. For example, if I posted revenge-porn of you on lemmy (or any personal information), you would have the right to demand it being deleted.
Is that not a correct interpretation?