“[t]he more an owner, for his advantage, opens up his property for use by the public in general, the more do his rights become circumscribed by the statutory and constitutional rights of those who use it.” -- Justice Hugo Black, majority opinion in Marsh Vs Alabama.

Youtube et al certainly encourage the free and public flow of traffic. Their business model depends on it. So their responsibility to the public would seem to obviously overshadow the perceived protections as a "private company".

I was also a child of the 80's