Earlier quoted context omitted.
Now, for morality to be on their side, they need to publicly advocate and work on a better way to remunerate the content creators. Of course, they could go rogue and act exclusively out of spite for big media, arguing parasitically that how the content creators make money is none of their business. But I really hope they don't.
Or they could correctly argue that the existence of big media is a massive net negative for the welfare of humanity, and anything that diverts money away from the industry is good for the world. Not that piracy seems to put much of a dent in the revenues of Hollywood, unfortunately, but if it did, that would be more than adequate moral justification for supporting Popcorn Time.
What do the revenues of Hollywood have to do with anything "moral"?
"Hollywood" (or the movie industry) is a risk taking enterprise. They put money up front to create art that they believe will offer a positive reutrn for their investment. Sometimes it produces good things, sometimes it produces dreck.
The question is, why does Hollywood need to fail for a moral victory? There are a variety of routes to produce and distribute your own film, go ahead and do it. Hollywood doesn't preclude you from making a successful independent film anymore than Microsoft precludes you from making a successful software application. Adam Carolla just crowd-sourced his latest film based on a script.
Of course, in the case of independent anything, you get/have to take all the financial risk up front. That's a downer (or impossibility) for most people, and partially why Hollywood exists.