Emmet, not to belittle your comment but it's giving the bow too much credit and not enough to properly spined arrows. Having the arrow lining up straight only refers to a cut to center bow.
IMO, until first brace, when the bow is under tension, you can not know how the string aligns.
Also, if the handle is not in alignment with the rest of the bow the string alignment can look off when it is only the handle that is not in alignment.