The purpose of a documentary is to educate viewers. If people are not entertained that is okay, but if the don't go away educated in some way it failed.
The purpose of a movie is to entertain, so it if isn't entertaining it also isn't good. It might also be educational, but that isn't the purpose.
What documentary directors know is that if you are not at least somewhat entertaining viewers will not watch and so they put in some entertainment aspects even though that isn't the purpose. Movie directors know that they need not tell the truth, though often they will just because viewers will believe the movie and potentially change behavior despite that not being intended and so morally they sometime feel a need to show someone doing something that works even though it isn't required and some do not.
Of course where the line is, is often blurry. Some movies are intended as documentary except that they are propaganda and so we would call them fiction. Many documentary are primarily entertainment, with the minimum education to claim documentary.
Rocky was clearly intended as an entertaining movie. The directors put enough effort into finding truth about boxing training that you won't go too wrong treating it as a documentary - but if you really want to be a boxer there are better sources to learn how and you will discover some things they got wrong for plot reasons.
The purpose of a movie is not to entertain. Or rather, that is one possible and valid and fine purpose, but it is certainly not the only such purpose. To believe that it is, THAT is the real confusion.
The difference between a documentary and a movie isn't about purpose, it's about method: how they try to get at the truth. The documentary tries to do it by looking at a specific case; the movie (and fiction in general) tries to get at truth via an imagined aggregate (although of course usually embodied in a single fictional character, like Rocky).
There is a guideline that says "don't be snarky"[0] and I think it applies here.
Having produced a documentary (and being in the process of creating another one), I can't say that I agree with your view on purpose at all.
The purpose of either documentary or fiction movie is whatever the movie maker aims at. There is no reason for anyone to abide by your standard of "trying to get at the truth" when writing the scenario for Once Upon A Time in America, Jurassic Park, The Simpsons (the movie), or Bowling for Columbine.
I'd say most movies have an intent behind them. Further than that, we're art amateurs trying to interpret the meaning of abstract paintings in a gallery. Maybe the painter wanted to denunce the patriarchy. Or maybe they had food poisoning that day. Who knows.
The movie doesn't have to. The documentary cares about engagement.
edit: you would actually rather watch a version of rocky where they show thousands of hours of running? this sounds like nonsense
And, let's be honest, someone somewhere will watch it.
And make a YouTube reaction video of themselves watching it.