Yes that is very real! You can actually be sent to jail for downloading or watching streaming video clip of content that is covered by copyright infringement. This is specially the case when you download the streaming content from heavily protected legal sites like the official movie trailer site of some movie. Say you want to watch a martial arts film and you download a martial arts video clip form the site that clearly says DO NOT. You could very well be sued for copyright infringement. 

If you download funny video clip from sites that broad cast them directly in real time with TV, which in itself is illegal, unless it an official site, then the joke will be on you when you are sued for illegal viewing or download or media. Also watching uploaded some spicy content like sexy utube video that is covered by the copyrights of a particular site and then downloading them could effectively sue you and send you prison in most extreme cases. 

All this is in the efforts to regulate media on the internet and prevent piracy of information. This is because through pirated videos, the makers or distributors of the clips do not earn anything. With more and more distributed free copies, the industry starts loosing profit and very soon the industry is a victim of huge loss. The site that steam videos or upload user videos urges the users to exercise moral discretion not to distribute copyright videos and illegal videos on the internet.