There is a big difference between the first amendment free speech and censorship by private organizations. The first amendment protects against government intrusion into speech activites. Hence, if youtube was a government run organization, the removal of the posting would violate the first amendment protections on free speech per se. This isn't so for private corporations, which is why your company can fire you for abuse of email privilages. Since youtube is run by google, and google is a private corporation, youtube can restrict access to the forum as long as it doesn't do so based upon classes of people entitled to protection [which is a separate part of the constitution BTW].
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There is a big difference between the first amendment free speech and censorship by private organizations. The first amendment protects against government intrusion into speech activites. Hence, if youtube was a government run organization, the removal of the posting would violate the first amendment protections on free speech per se. This isn't so for private corporations, which is why your company can fire you for abuse of email privilages. Since youtube is run by google, and google is a private corporation, youtube can restrict access to the forum as long as it doesn't do so based upon classes of people entitled to protection [which is a separate part of the constitution BTW].