Predicting on Correlated Units

I have an OLS regression model built from independent xi- and yi-variables. The i-units are sufficiently spatially separated to be uncorrelated.

The task is to use the model to predict values on a grid where the neighboring grid cells are strongly correlated in all x-variables. I have been told this shouldn't matter -- can anyone confirm or provide some support for that claim?

Global Moran's I (for one of the x's) on the original units is 0.15 and on the prediction units is 0.67. There is no chance of getting y values in the neighborhood of the original units, though if it would help, the x's can be calculated.