Simultaneous vs Non-simultaneous confidence bounds in the curve fitting toolbox

Can someone help me to better understand simultaneous confidence bounds in the curve fitting toolbox? The meaning of the non-simultaneous bounds is clear. What I don't understand about the simultaneous bounds is the following: "Simultaneous bounds measure the confidence that a new observation lies within the interval regardless of the predictor value." This is counter-intuitive to me since when the simultaneous bounds are plotted, the value still varies with x across the data range. It would appear that the x value still influences the bound. Can someone explain the meaning of the simultaneous bounds in a different way?

[Brian]

I think I may have just figured this out. Is this just that the confidence intervals are adjusted so that the stated confidence level is the same for all predictor values at the same time, i.e. instead of each point having a 95% CI, the CI for all points simultaneously is 95%? In other words, for the non-simultaneous CIs if we had the 95% CI for two different points, then the overall probability of observing a value at those two points outside of the CIs would be more than 5%. The simultaneous bounds are corrected so the probability is 5% everywhere at the same time. Is this right?

[Martin Hoecker]

According to the Wikipedia article on confidence and prediction bands you appear to be right. But it is confusing that the "simultaneous" prediction/confidence bands are bands at all. As far as I understand it, you have to "remeasure the data"/"predict the true data" at the same x-points as before! Therefore, the simultateous "bands" should only be plotted at those original x-points!