I feel I should explain a bit further:

Why would you want fletched and unfletched shafts to hit the same spot?
Who cares? Won't we always shoot with fletched shafts?

The reason is this...
If they are hitting different places, then your fletching is compensating for some mismatch of forces within the bow/arrow/shooter system. The bare shafts are showing you the raw data (what the arrow wants to do from being acted on by the bow and shooter, a scientific 'control' if you will), and the fletched ones are showing you what your fletches are doing to the arrow's flight because things aren't right.

You don't want to rely on your fletch to get the arrow going in the right direction with the right orientation. The shaft's spine, rest, your form, and stuff should take care of that.The fletch is just there to keep the arrow on it's path and provide stability once it's in flight.

Even if you are shooting bullet holes in paper, you can still have a foot or more of difference in point of impact at 20 or 30 yards. When you bareshaft it down to hitting the same spot, paper will still show you a bullet hole.