[brudgers]

>"Given enough back-and-forth communication, however, a human will always realize that the bot is just parroting words and phrases that are statistically relevant to the human's questions."

That however is not the Turing Test at all. Here is what Turing actually wrote:

    I believe that in about fty years' time it will be possible, 
    to programme computers, with a storage capacity of about
    109, to make them play the imitation game so well that
    an average interrogator will not have more than 70 per cent 
    chance of making the right identication after ve minutes of 
    questioning. 

http://orium.homelinux.org/paper/turingai.pdf