NFL goal line spot

Question
When the Patriots were inches short on a play that had been called a touchdown the referees spotted the ball on the 1/2 yard line. It was only inches away when the runner went down and if it hadn't been called a touchdown originally I assume that they would have used the actual position of the ball inches away from the goal line. Why punish the offense like this?

Answer
John
you assume correctly. They spot the ball where it is down per the replay.  Many times when the ball is to be placed inches from the line to gain or goal line the referee announces the ball will be placed at "the half yard line" or the "foot line".  This is just meant to communicated it is less than a yard to go for the line to gain or goal line. As you know the field is marked in yard lines [not half yard lines or feet].   Also remember the ball must be snapped backward, so the original position of the ball where spotted might be 6 inches from the line to gain but after the backward snap the ball is at least a yard behind the original position.

You are correct with your assumption the ball is actually spotted at the actual position where it became dead.  It is just is not announced the "ball will be placed inches from the line to gain".  The offense is not punished or cheated.