This is only true for a masthead rig with a very stiff mast.
It is true of any sail whose luff is attached to the mast or forestay. If the mast bends, it does not appreciably change the distance that halyard must travel up to top of the mast and down to the head of the sail. Bending the mast does not change the length of the mast.
If the halyard is internal, it is technically true that when the mast bends the halyard can take a shorter route to reach the top of the mast - simply because the halyard's diameter is smaller than the interior of the mast. But that effect is
really slight at the curves possible on any rig and certainly at the curves a cruiser is likely to use. I just did a quick calculation, bending a 40-foot mast 12 inches abaft - which is a pretty big arc. In that extreme condition, the distance the halyard needs to travel is just 0.7 inches less than when the mast is straight. At a more modest 6-inch deflection, the difference is about 0.2 inches.
Again, talking about cruisers ... this is so close to nothing as to not warrant attention. If the halyard is external, there is virtually no change even at the extremes because the halyard must still go the same distance.
To be honest, most racers I know are not effective enough at sail trim that this makes any difference for them either.