Here we go again. Stop using the word 'center' for crying out loud. Understand my stance better and maybe you'll be able to answer the question yourself.
I think I finally understand why you don't understand why everyone is characterizing your argument as center of square to center of square. You have not actually tried what you are discussing.
Go get a battle mat. It doesn't matter which one, as long as it is equal squares.
Now mark an X to represent an NPC somewhere in the middle.
Move 30 feet due east on the map (6 squares), then one square up. Mark a Y in this space to represent the charging PC.
Now take a straight edge of any kind, and draw a line from the upper right corner of the PC square to the upper right corner of the NPC square.
Notice that the line you just drew does not in fact go through the square directly due east of the NPC...which is the square you are arguing this PC *MUST* charge to. If you measure from the upper right corners, then going "directly towards" the NPC would not land you in the space you insist must be the place you attack from in this senario.
Now do the experiment again, this time drawing a line fron the upper left corner of the PC to the upper left corner of the NPC. Notice again it doesn't go through the space you believe you must charge to.
Do it again, this time from the upper right corner of the PC to the upper left corner of the NPC. Again, it doesn't touch the square directly east of the NPC.
What this experiment should prove to you is that, unless you are arguing that it is center point to center point, your argument does not hold up. Either that IS what you are arguing, or else you have a faulty argument.
So which is it. Do you mean center point to center point, or do you mean any point in the PC square measured directly towards any other point in the NPC square. If it's the former, then stop denying it. If it is the later, then your arguement doesn't work. Pick one.