The most blatant of all is that Popcorn Time is not a site, it's an application (which is why it's been so hard to block).
It uses existing sites (like YTS and The Piratebay) to find magnet links to content to stream (using a torrent streaming library)
Also: "“Mr. Robot” is not available elsewhere, apart from on Popcorn Time." - What the hell? If a series is available on Popcorn Time it's inherently because it's available somewhere else, as they don't host any content
But the one that bothers me most is that they mention how before Popcorn Time, piracy involved: "Aggressive advertising banners, websites popping up unexpectedly and strange porn ads".
Well, guess what? Popcorn Time is an application that most people download in binary form, so it could steal your personal data, inject advertising in other sites, use your computer as a proxy... etc. It's not a step forward.