Really, it's true. You'd need a very accurate scale to see the weight loss, but two people standing close together weigh slightly less than two people standing far apart because the gravitational attraction between them actually reduces their mass.
Matter and energy warp the geometric fabric of space and time. What we perceive as gravity is the space-time distortion produced by energy or mass. Gravity provides a negative contribution to the energy of any pair of objects, and it becomes more negative as they get closer.
If you take a rock and carry it to the top of a cliff you expended energy when you lifted it, you gave the rock energy. When you throw the rock off the cliff gravity makes the rock fall, it looses the energy you gave it. Gravitation has a negative effect on the energy level of the rock. But you have to fall for someone for that to be true.
Because of E=mc2, negative energy is equivalent to negative mass, so the gravitation attraction between two people just standing close together reduces their mass. They weigh less than they would if they were weighed separately far apart.