You're missing the fact that how much Joe values the surgery depends on whether or not he expects to be told whether it worked afterward. If Joe expects to have the surgery but to never find out whether or not it worked, then its value is U(0.5)-U(0)=0.25. On the other hand, if he expects to be told whether it worked or not, then he ends up with a belief-score or either 0 or 1, not 0.5, so its value is (0.5*U(1.0) + 0.5*U(0)) - U(0) = 0.5.

Suppose Joe is uncertain whether he's attractive or not - he assigns it a probability of 1/3. Someone offers to tell him the true answer. If Joe's utility-of-belief function is U(p)=p^2, then being told the answer is worth ((1/3)*U(1) + (2/3)*U(0)) - U(1/3) = ((1/3)*1 + (2/3)*0) - (1/9) = 2/9, so he takes the offer. If on the other hand his utility-of-belief function were U(p)=sqrt(p), then being told the information would be worth ((1/3)*sqrt(1) + (2/3)*sqrt(0)) - sqrt(1/3) = -0.244, so he plugs his ears.