if your batting says quilt every 4" that does mean---in all directions---if you leave your 2 1/2" borders totally not quilted the 2 1/2" part is fine...but what about that length??? is it less than 4"? you need at least a line across every few inches to keep the batting from pulling apart and bunching up in the borders when laundered.
if you do not want to quilt areas of a quilt it is best to use flannel or fleece for a batt- which will not pull apart and does not have any specific quilting requirements