I don't believe that is true.
In order for light to be affected by gravity wells, gravity must travel faster than light.
If, in fact, gravity travels at all. It's kinda like saying magnetism travels. It's just a static field that gets weaker with distance.
What happens when one turns on an electromagnet? Surely the force travels from one point to another.
Or when two enormously massive objects such as neutron stars or black holes collide. Prior to the collision, their gravitational fields are different than they are afterwards, and the newly created combined effect is propagated outward into space.