I do not see how your first and second sentences are related. I might agree with the first sentence, but I do not agree with the second.
For example if I said "After this interview, before I put you to sleep, I will torture you with probability equal to the square of 1 minus the probability you give to the truth." If she estimates 1/2, she will say 1/2. If she estimates 1/3, she will say 1/3.
Edit: I interpreted your question as a rhetorical question implying that she would no do anything differently.
I should clarify. The universe doesn't ask you for numbers or ideas, it's your behavior that matters. Your example makes sense in a psychotic simulation, of course. Hopefully we are not living in one.
I got into a heated debate a couple days ago with some of my (math grad student) colleagues about the Sleeping Beauty Problem. Out of this discussion came the following thought experiment:
Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: She will be put to sleep. During the experiment, Beauty will be wakened, interviewed, and put back to sleep with an amnesia-inducing anti-aging drug that makes her forget that awakening. A fair coin will be tossed until it comes up heads to determine which experimental procedure to undertake: if the coin takes n flips to come up heads, Beauty will be wakened and interviewed exactly 3^n times. Any time Sleeping Beauty is wakened and interviewed, she is asked, "What is your subjective probability now that the coin was flipped an even number of times?"
I will defer my analysis to the comments.