Because being on the receiving end of a public broadcast does not give you the right to re-use the content. The content owner, for better or worse, typically retains the exclusive right to use or broadcast the content, regardless of how many times it is broadcast.

Consider older mediums; does broadcasting a TV show put it into the public domain? Or playing a song on the radio?

Well the tweet is under whatever terms Twitter imposes on you for using their service. But in this particular case, someone tweets a photo some other origination copyrighted.

I mean, technically taking a photo of a movie poster and tweeting it is infringement, but most movie companies have better things to do than go after you for it, especially if it's not disparaging and may promote the movie.

Twitter isn't quite an open broadcast, and even if it were it wouldn't necessarily mean it was entered into the public domain. A recording of a musician's public performance of their song is still under copyright; MLK's "I Have a Dream" speech is under copyright; literal broadcasts (TV/Radio) are still under copyright.