Imagine if someone has their Blu-ray player playing on a TV. They design a system that flashes physical flashcards in front of the TV with a twitter feed. That shouldn't be illegal, right?
Now, what is the difference between that and overlaying a digital twitter feed? You are legally allowed to view the content. Why shouldn't you be able to consume it in any way you deem fit? If you copy or distribute it, that should be (and is) a crime, but until you have done that, in my opinion you have done nothing wrong.
Corporations have successfully lobbied to erode the whole basis of our legal system by taking away the presumption of innocence at every turn.