As an example of an array that fails in this regard, take:
9 5 1 6 7 2 4 3 8
While 6+7+5=18 is in fact a multiple of the 9 that it surrounds, as required, the 2+7+3=12 that surrounds the 8 is not a multiple of 8, so this grid fails (it also fails based on the surrounds of 6 and 7).