Copyright is the right we give to content creators so that they can financially benefit from their work. It is not a generic "I control everything I have ever said" power.
In particular, "fair use" specifically doesn't require people to get permission from a copyright holder:
Discussing the tweets of public figures is clearly "commentary and criticism", which would give things like PostGhost "substantial non-infringing use" (which I believe is the relevant legal threshold).
In particular, "fair use" specifically doesn't require people to get permission from a copyright holder:
http://fairuse.stanford.edu/overview/fair-use/what-is-fair-u...
Discussing the tweets of public figures is clearly "commentary and criticism", which would give things like PostGhost "substantial non-infringing use" (which I believe is the relevant legal threshold).