On the surface it seems open sourcing documentaries is not difficult. Just put it under the right license and publish. But there are some problems to it.

First the thing you have to do with all things, if you want to open source them: release also the source. For an documentation this means the raw shootings without color and brightness adjustments you made later and without extra audio tracks like music you put in the background. The music you put in the background should be also available in the sources, but separated. Probably source material for animations or graphs you put into the movie. For all parts you need the consent of all contributors to make their part of the work open source.

But that is not all. You have to consider that more than just copyright influences restrictions on creative works. In many area of work much of them doesn't matter, but documentaries touch some of them. And all naturally depends on the exact law in the jurisdiction you live in (or the one you shoot the movie).

One is discussion in the european union at this point. A new proposal is discussed by some under the angle that it might restrict the freedom of panorama in the european union. Freedom of panorama means you can photograph or film stuff that is owned or copyrighted by others as long as this is in public places and include it in your publication. That includes buildings. If that is allowed or not is different in different jurisdiction (and may change over time as the example of the european union shows). Such consideration alone can make it nearly impossible to shoot footage in a city.

If you shoot it on non-public places Freedom of Panorama doesn't work, that can even hit you in surprising ways. For example, I live in Potsdam. We a historic park, Sanssouci Park. That park can everyone go to, but it is not officially public, as it is owned and attended by a foundation. That foundation made news, as it sued different photographers for taking pictures in the park and selling the photographs. Many aren't aware that the freedom of panorama isn't working in the park, as the photos in the Wikipedia demonstrate.

Even if you try to get consent from the owners, it will be more difficult for open source movies. Because it includes that everyone can redistribute or alter the images. Many that might be OK with a one-time publication might have reservations against the open source rules.

But there is another problematic part. Think, you make an interview with someone and include it in your documentary. If that is open source, the license allows everyone to change it. That means, malicious people could synchronize other texts to the persons sayings and therefore completely alter what he/she said. That usually is prevented by Personality rights. Again, these laws can be very different in different jurisdictions. But usually you cannot alter footage to denigrate someone on these footage. As you basically cannot prevent this, you should add a disclaimer, saying that some changes that might be allowed by open source might still be illegal and declare that you have no influence onto other alterations of your work.

To address what Philipp said in his comment on the question, I would add that this is a smaller problem. Sure, everyone can change your documentary and the result isn't telling the truth anymore. That is right, but at the same time the derivate isn't exactly your documentary anymore, and we should be accustomed to the fact, that others don't always tell the/our truth.

In the end, the safest way to make an open source documentation might be shooting animals in the wilderness.