Of course folks should have the right to post videos on the internet. What they should not be doing is posting videos that include or are about other people without their consent. That is a violation of privacy and needs to be open to prosecution. That's especially true with regard to explicit videos.
People should have the freedom to post videos online. This is a no brainer or rocket science question. The video should however be approved by the audience and show content that is not pornographic or offensive if displayed for instance on youtube. This is America and people have the freedom to post whatever they want and can do so anytime.
This is not only talking about Americans. Also, freedom of speech does not cover certain things, I do not have the right to call someone something they are not, and neither do you. If you create the website, you chose the rules. But is you use someone else's website, you abide to their rules, and if you don't like those rules, too bad. Even in America, you do not have the guaranteed right to freedom of speech on youtube, as the first Amendment only provides that the government (not a private company such as youtube) may not take away your freedom of speech (except slander, libel...)