That's ridiculous. By the same logic, that's like trying to ban DVD players because they too can technically play copyrighted material...
Popcorn Time only sources torrents from illegal sources i.e. does not have significant non-infringing utility.
That's where the distinction comes in.
If it was similarly limited to only play legal material (or even indiscriminately play material from a source that contains both) this would never have been an issue.
I know 'MUH FREEDUMS' is pretty big around here but the fact is that this was rather blatantly illegal and takedown should be expected. Their website explicitly and exclusively shows content that they do not own: http://www.time4popcorn.eu/
The takedown request was not because the screenshots are copyrighted. That is not the infringement. If you don't understand that then you might want to read a bit more before becoming involved with the grown-ups.
I don't need a source to prove it. The comment speaks for itself.