In the age of Twitter, such hijinks are amplified further due to their world-readable nature. The problem with innocent, uncomfortable-but-well-intentioned jokes is that you have to consider how it will play with someone whose job it is to flag up and respond to any and all threats, no matter how credible.
Fundamentally it's your joke versus a member of staff who is not in a position to deviate from the procedure and brush it aside.
Plus, who'd want to be the guy who gets their face on the news after an incident because they ignored a threat and thought it was a joke? They won't, and often CAN'T, take that risk - they are simply not in a position where they are allowed to do so.
As you say, we live in shitty knee-jerk reactionary tines, but whatever the rights and wrongs, in this kind of situation it's prudent to moderate one's comedy appropriately.