The scant quarter inch is used to accomodate the minute space taken up by the fold when two pieces are sewn together. The accuracy of the finished piece is what is important. If a pattern uses 2" squares and you sew right on the 1/4" line and sew two together then depending on the weight of the fabric, the finished square might not be exactly 2" finished. This is why it is important to test your seam allowance at the beginning to assure the finished piece will be the accurate size. If you are sewing only squares then it is not important as long as the seams are consistent. Machine manufacturers all have a 1/4" foot but not all are created equal so it is best to test the foot.
If you take two strips each 2.5" wide and sew them together the results should be 4.5". If not, then one should adjust by moving the needle or other adjustment. Sometimes the size of the needle or the weight of the thread can effect the accuracy.
All these things should be done to make sure all pieces fit. Adjustment for accuracy is especially important if you are sewing triangles together and then to other shapes, rectangles to squares, etc etc.
Accurate piecing reduces the frustration in trying to fit pieces and blocks together.
The same rationale applies to which side of the marked line on your ruler. If you cut on the right side, the piece might not be accurate. It could be a "scant" less than what it should be. Add this "scant" to the full 1/4" seam could give major problems.