I also find it hilarious how far people will start to peck at you based off their own assumptions. This is a reason I find memes fantastic for replying to these type of posts with. Being more snarky, witty, and just having fun with them when they're the ones that came onto my page and posted on my tweet.
Reminds me of a story my dad told me. Jeff Dunham came into town to a place called Laughs, it was a comedy club type of venue that's been closed down for a long time. Dunham brought out Walter and was doing his jokes when some guy was heckling, he was drunk as well. He started arguing with the puppet, to which Walter looks up at Jeff and says, "He thinks I'm real." The entire place busted out laughing.
Twitter is an all out, no-holds-barred, arena of words. If you do not have tough skin, you are going to be devoured and your blood plastered on the wall for all to see, humiliated, and picked pieces off of by the vultures.