Think about how outdated a bat signal is, why can't batman check for tweets?
1. It's inherently asymmetric (Batman can observe the message but messengers cannot observe him).
2. It's highly unlikely to be forged.
2.) I'm pretty sure that what seemed like a good third of the sixties Batman TV show episodes involved Batman showing up to the Bat Signal only to have it have been a trap. (and yes, I consider the TV show to be the canonical Batman).
1. It's inherently asymmetric (Batman can observe the message but messengers cannot observe him).
2. It's highly unlikely to be forged.