I play it just like you do when you "spot" a ball.
If you can't spot the ball in the "center" of the spot, the ball is spotted behind it.
You never spot a ball on the front edge of the spot and consider it "spotted". You place the "center' of the ball on the "center" of the spot.
Therefore, the center of the ball should be what is considered when placing the cue ball on the head string.
How can the "center" of the ball be considered as the reference point on one end of the table and not the other?
If you can't spot the ball in the "center" of the spot, the ball is spotted behind it.
You never spot a ball on the front edge of the spot and consider it "spotted". You place the "center' of the ball on the "center" of the spot.
Therefore, the center of the ball should be what is considered when placing the cue ball on the head string.
How can the "center" of the ball be considered as the reference point on one end of the table and not the other?