The correct statement that explains how the magnet is able to stick to the refrigerator without directly touching it is: "The magnet’s magnetic field can act at a distance, and influence the metal of the door through the picture."
This statement accurately describes the nature of magnetic forces, which can exert influence over a distance. The magnet's magnetic field can interact with the metallic surface of the refrigerator, allowing it to stick even though there is a picture placed between them. The other statements do not accurately describe the interaction in this scenario.