The quotes you gave were certainly relevant, but still: Turing doesn't state in his paper that the interrogator is to be made aware (all I said). The rest is our modern interpretation of the test. It's a fine interpretation that I don't have a problem with, but it is an interpretation, not a criteria lifted from the paper.
In the article Kurzweil even says as much: Turing was carefully imprecise in setting the rules for his test, and significant literature has been devoted to the subtleties of establishing the exact procedures for determining how to assess when the Turing test has been passed.
It is not made clear in the paper that the intention is for the human interrogator to be made aware of possible replacement. I myself know this is not the most popular interpretation, but it still makes sense as a Test, you just check if player C is wrong as often as before. Some research has shown that unaware people change their attitude and questions, while other research has shown that for some judges this doesn't matter. Early Turing bots were tested under the interpretation that judges can be unaware. For sourcing on this see: http://en.wikipedia.org/wiki/Turing_test#Should_the_interrog...
I think one of the problems with the Test is that it was written by a mathematician and logician, while it touches on fundamental philosophical problems of consciousness and other minds. It may be valid in these pure domains of information theory, while it may be problematic in philosophy of mind. It is not sure where one ends and the other begins. Philosophers hone in on the ambiguities and omissions. They ask: "Why would Turing omit this rule, while carefully stating other rules? Is this ommission significant? Does the outcome of the test change when we make people unaware?" That is not bizarre, as much as it petty.
Another problem I see with the Test, and this may be controversial, but: Turing creates a test for intelligence and as the basis he takes the distinction between male and female. Then he replaces the male with a machine and asks us: if we lose our gender guessing game as often as before then machines can think. This assumes that Turing thought that he could distinguish males from females by questioning their intellect (as for small-talk both players could easily lie about that). Which at the time of the paper may have been realistic, but in modern times is not the case: If you have an adversarial male and a female who try to trick you, I don't think I could make a distinction at all: My guess would be as good as random.