If a website User uploads video, onto the website, of someone who agreed (verbally) to be filmed (and also was told that the video will be displayed online), do you think the website could be held liable for publishing the video if, prior to uploading, the User had agreed to the website Terms that essentially state "user will not upload content that is not lawfully users to upload to the website"?

It seems to me the website would always first be asked to remove the footage, prior to any legal problems. What do you think?