When you say "rendered to a screen", do you really mean "placed on a webpage"? PDFs generated by LaTeX are rendered to screen all the time.
edit: Actually, I find that I completely agree with your point if "printed" is replaced by "shared in pdf format" and "rendered to screen" is replaced by "shared in plain text or HTML format".
I'll have to think about this further, but at first glance this seems like a better heuristic than what I wrote.
There's a little bit of opinion embedded in my original post, which is that PDF is an inappropriate format when intended for screens. It's okay if you're wanting to provide a primarily printed document on the web or in email, it's okay, but if your primary target is screens, PDF provides a pretty poor user experience.
edit: Actually, I find that I completely agree with your point if "printed" is replaced by "shared in pdf format" and "rendered to screen" is replaced by "shared in plain text or HTML format".