Mike
As far as exact interpolation, please reference the following image. 2 cells of a raster, white equals the cell center and red is the sample location.
Predictions are made at the cell center and that value is assigned to the whole cell.
When predicting the value for the upper cell, 1395 will carry the most weight and therefore the cell's value will not be equal to 1395. However, 3199 falls exactly at the center of the cell and therefore that cell's predicted value will be equal to 3199.
The smaller the cell size the closer the predicted cell value will be to that of the sample point
Regards
-Steve