Actually, this has nothing to do with freedom of speech, and even Google's terms of service are irrelevant. Here's a very simple scenario that results in hauling Google and/or Google's partners into court:
1. Alice produces a video consisting of 100% original creative content, and registers copyright to it.
2. Alice licenses the video to Bob for distribution, under terms which allow uploading to YouTube.
3. Bob uploads a copy of the video to YouTube.
4. YouTube flags the video and declares the copyright to be held by someone other than Alice.
5. Alice, who is not bound in any way by Google's terms, heads down to the courthouse with a copy of her registration papers and files suit over the misrepresentation of her copyright.
1. Alice produces a video consisting of 100% original creative content, and registers copyright to it.
2. Alice licenses the video to Bob for distribution, under terms which allow uploading to YouTube.
3. Bob uploads a copy of the video to YouTube.
4. YouTube flags the video and declares the copyright to be held by someone other than Alice.
5. Alice, who is not bound in any way by Google's terms, heads down to the courthouse with a copy of her registration papers and files suit over the misrepresentation of her copyright.