Early on the article claims "Apple tells CNET that it won't delete your movies, either. At least, not ones you've downloaded.". But that's not a useful answer because it doesn't provide any real security about one's downloaded works.
Later CNET says "We can't be sure what will will happen if Disney -- or any other content provider -- "recalls" a digital purchase, as a publisher did with an ebook of George Orwell's 1984 on Amazon back in 2009.".
Keep in mind that Amazon made a similar pledge to what Apple reportedly told CNET. As Richard Stallman rightly points out in https://stallman.org/amazon.html "In response to criticism, Amazon promised it would never do this again unless ordered to by the state, which I find not very comforting.". In other words, Amazon tacitly acknowledges it retains the power to do this again.
It's far more useful to examine the situation along the lines of which party retains what power over the user, or to look at how much freedom users have in the situation.
Therefore the real hinge here (which goes completely unaddressed in the CNET article) is software freedom (the freedom to run, inspect, share, and modify published computer software). If one uses free software to locate and read/play the work, then one has a chance to make sure that the free program won't betray their interests -- continuing to read/play the work at any time, for any reason, and do so without spying on or reporting the activity to others without explicit consent from the user.
But if one uses proprietary (nonfree, user-subjugating) software to access a downloaded copy of the work, one's access to the work is in jeopardy. One can't be certain that copy will be readable/playable through that proprietary software. Perhaps the proprietary software will delete that copy of the work (putting aside what's legal or, more importantly, ethical for the moment, it is worth noting that proprietors retain the technical power to do exactly this in most people's common use of media). Perhaps the proprietary software will report on the user's attempt to read/play the work thus notifying someone what's being read/played and from where.