No, censorship is the suppression of information based on content, not ownership.

Many people believe that censorship applies only to speech limited by a state actor. Ex: the first amendment of the US Constitution means that the US government cannot repress your speech. It does not prevent others from doing so.

Many other agents engage in repression of speech: we repress ourselves, so do parents, friends, communities, lawyers, contracts. We don't automatically regard repression of speech/expression as a bad thing, and in many cases we are glad for it.

Interestingly, in some (all?) European countries uploading the recording of your speech (or just you as a person) on YouTube would be a violation of your privacy rights, unless you're a person of public interest and gave that speech in public, i.e. in front of a crowd or something similar.