The other day I was watching Turistas on TV. Since I had already seen this movie some years ago, I could quickly notice that several scenes were not being shown [censored]. Turistas is one of those movies where these explicit/horrifying scenes are central to the story and experience of the movie. If cut, the movie feels as Coke would if sugar is removed from it. So for someone who hasn't seen this movie before, watching it on TV would make it seem like the movie isn't as good/impressive/entertaining as was claimed by someone who has seen the full movie previously.
Herein comes the idea that if/when censorship of a piece of content [movie, advertisement, book, article, newspaper, video, song, SERP, website, etc.] is done, it should at least be conveyed to the users that such censorship is in force on the content being consumed currently, so that the users don't wrongly/unfairly get an incorrect impression that the piece of content in question isn't as interesting/entertaining/shocking/strong as was claimed by others [who had consumed the full/unabridged version].