You did everything perfectly Stu. Theres one thing you need to make sure of that you can check, - did you set the colour sampler sample size for 3x3 average, or a point sample?
Its important NOT to use point sample. When I did threshold I found the black as you did, and the whitest in the stripes, - BUT the stripes were way too narrow to provide a 3X3 sample size, so I used the next largest white are by dragging the slider in a littlem and that was the cloud on the book. When you are selecting the white point, hover the sampler over the white you intend to select and take a look at the 'info' palette, - it should indicate 255,255,255, - if not, then though it looks white, you will sample something thats not entirely white. Same for black at 0,0,0.
If the image you worked on was larger than the one uploaded, you may well have identified white prperly with the stripe, and it would have supported a 3X3 sample.
Assuming you did all this correctly, then I would use colour balance to balance red towards cyan anyway, as I have done. I do this because even with a colour correct shot, I fell my Canon 5D over saturates red especially in skin, and your cam might do the same. By the way, - take the shot in RAW, not jpeg if you can, then you dont have to correct the jpeg settings the camera will apply.
Theres an excellent book on digital colour called SKIN you should try to get you hands on, - its fantastic.
Youre on the right track, - keep it up,
Hope this is useful,