I don't know about other projects, but the English Wikipedia imported a large amount of text from an out of copyright encyclopaedia, the 1910 version of the Encyclopaedia Britannica. I'm sure much of that is still there, and while the writers of it will be long dead they probably weren't anyone's volunteers at the time, certainly not ours. We also incorporate lots of quotes, especially if they are out of copyright.
You can sort of shuffle round the spam problems that Kudpung mentions because they are mostly unwanted and not part of the design (though we are happy if someone with a conflict of interest posts a suggested extra paragraph on a talkpage and another editor makes it more neutral and adds it to the article.....).. But the out of copyright public domain bits, those are part of the design ‘All of the articles on Wikipedia are written by volunteers’ is not a statement that fully reflects our aims as a movement. Remember we are part of the open source movement, and much of our content especially the images but also some of the text is from other open sources. If we try to imply that we think of wikipedia as only feeding into the pool of open source material and not receiving and using openly licensed material from others then we undermine our role of being aggregators and editors as well as writers and photographers.
That said if the video contains the phrase ‘All of the articles on Wikipedia are written by volunteers’ I managed to watch it twice and blink and miss it both times. I liked that video, thanks for doing it. If I was going to be pedantic about it I'd point out that people do come to Wikipedia every day trying to slant it or hide things, but we have a large community of volunteers who resist and usually revert that. Also it was great to see the confidence of people saying that everything was sourced, and of course if you add info and want it to stick you need to source it. However we are a long long way from moving from our policy of verifiable to one of verified, let alone of finding sources for the vast amount of unverified information that we already have.