The body aligns parallel to the target line!
It is vital that your shoulders, hips, feet and arms are set up parallel to the target line for the following reason.
Think about your putting stroke this way: the shoulders swing the arms and the arms swing the putter. If the shoulders are not parallel to the target line then the arms will swing on a path that does not run parallel to the target line. This means that the path of the putter will also swing on an incorrect path and therefore the ball will start off line.
To correct this error you will have to either manipulate the face of the putter or you will have to swing your arms on a different line to your shoulders. Neither option is satisfactory since poor mechanics lead to inconsistency and will break down under pressure.