It's the same reason why horoscopes and fortune cookies work. Stepping back and thinking logically, it's easy to see why their messages might apply to a lot of people. But when you're reading one, you can't help but think, "Ah! It says that I would encounter adversity at work this week, but overcome it! I knew that presentation wasn't the end of the world." And if you're a little lonely or down and need emotional rapport, you can't help but feel a little spark of excitement and connection when that Mechanical Turker claims to like your favorite TV show - especially because the text messages from the fake partner look just like they would from a real one.
No matter how deeply we trust our logical conclusions, our emotional response remains the same. We can't help but feel worthier when we're being praised (even by computers - see the Silicon Sycophants study: http://pdf.aminer.org/000/307/350/information_requirements_a...), hurt when we're being insulted, and connected when we're being connected with.