So basically Universal lied to YouTube and said the video was copyright infringement when it wasn't, and basically if SOPA passes Universal could do this to entire websites and not just single videos?
A better explanation would be that YouTube gave UMG (and other 'content' companies) a kill switch that works on any video and said 'Promise you'll only use this on stuff that infringes your copyright, ok?' UMG then crossed their fingers behind their back and said 'Sure, whatever.'
The second party of your comment is correct. SOPA would give these same companies a kill switch for websites instead of YouTube videos.
It's worse than giving them a kill switch. It even gives merchant account providers the incentive to take out "rogue" sites before they even get to make that request of them. The providers get to claim "immunity" from lawsuits if they "act in good faith" and take the sites out themselves before they ask them to.