I've seen people do it more than a few times.
They will tweet an angry, super-serious statement like, "How DARE anyone do this?" and the statement/pic/video they are responding to is completely innocuous. Here's an example.
They are apparently being sincere. That is, they are so wrapped up in their own ideologies they are angry about something that wouldn't make a normal person angry. Additionally, they just expect others to know what they are talking about.