This story about a social media persona gone wrong is an excellent case study for educators. Personally, when I do fiction on Twitter (as in the case of a fictitious dialog between a student and teacher - I always start by disclosing it.) Secondly, I don't think it is smart to mess with people by making things up. People need to be able to trust you -- especially if you want to be a credible academic source.
That said, read this so that when you see parody or fake accounts that you know they exist and you can also know that some people making things up for the fun of it.