Therein lies the problem. Interpolation tries to provide a value for the intervening space between point observations. Whatever interpolator is being used for a given point pattern and observation at those points will determine how an interpolator behaves. If!!! there is a spatial pattern in the data and the observation points are well spread out and sufficient to cover the area, then 'most' interpolators will return 'similar' results... note the quotes.
Your question was a bit confusing since you chose a natural neighbor interpolator which will produce a smoother surface (generally) than something like IDW, but inherent to it will be the fact/chance that the value returned by the interpolator and the actual observation will be the same. I suspected that you were more concerned by that issue... at point XY, the observed and calculated were different. This does not mean that the interpolation was bad, it just means that the surroundin data points included with point XY yielded that value.
Kriging in some of its forms, allow you to evaluate the underlying properties of 'how well' the interpolator worked for your data. It is comprehensive, yet it may not yield any better interpolation than other methods.
Now back to a plausible case... if you have a purely random phenomenon observed at locations in space ... no interpolator in the world is going to help and any 'calculated' value in the void between observations are pure conjecture, since the phenomenon is by definition, random.
So in summary... know your data, use the interpolator that best represents that data then decide if preserving the value at observation points is more important than having a 'calculated value' at those locations be different. You can get an interpolator that preserves the observed values, but looks ridiculous or you can have a cool looking interpolation that doesn't represent the observed points well or at all.
Sorry for the lecture, but interpolation should come with big warning labels
