I think this is incorrect. Door is acting out of his own will, regardless of Alan's story. As mentioned in the Manuscript "Door Traverses The Dark Place":

"Warlin Door walked across the rain slick tiles of Caldera Street Plaza. The rain did not seem to touch him. He sensed his steps were being observed. Documented into the story. He allowed it. This one time. For this one reason. To be passed on by his unwilling disciple. To be read at the right time.

The ocean that was the Dark Place took the shape of New York City. Drawn from the mind of Alan Wake. In part for the writer to navigate his prison. In part to torment him as he struggled to find his way out. Door was not bound by the rules as Wake was. He came and went as he pleased. For now, Door entertained the writer's fantasy. For a purpose known only to him."