I think the reasoning was to avoid cutting to close to the outside edge of the table into the side frame.I'm not sure I follow the reasoning on moving the pilot hole 1/4" from the original center. If the new cup holder is simply a larger diameter, the center point should still be the center point regardless of the size of the hole. Moving the pilot hole would actually shift the entire cup holder off-center relative to the original location, although that’s perfectly fine if the intent is to reposition the cup holder itself rather than just enlarge the existing opening.
I drilled mine centered on the original location, and they came out perfectly centered on the rail!
I could be wrong but since reading majority of the modified cup holders on these barrington tables, looks like they all used the the 1/4" off original center hole and it turned out all centered.
do you have a picture of yours by chance? just for reference.