I'd say most people have those options. But a journalist, who uses social media as an outlet for his/her job, should be a bit more judicious with how they use that outlet. Even professional athletes are finding their social media rants come back to haunt them, and they have zero professional responsibility to be decent, fair and able to communicate in a professional manner. But their employers are protective of the company image and take it seriously when their employees damage it with poorly thought out rants. Tim has the dual responsibility of being a journalist (who uses that very media as a professional outlet) and the reputation of his employer.
Perhaps Tim should have a professional persona, and one where he can be dickish with haters. But should he respond with his "work" persona, he should either take your option #1 or, better yet, have an intelligent dialogue with his critics---in the cases where that is possible. I admit it may not be for some---then he should resort to option #1. And, you know, it would't be the worst thing for Tim to, perhaps, admit he made a mistake in this instance. A little humility can go a long way.