What's the main clue for Rogues in the House being considered as a Corinthian story?
In a letter Robert E. Howard wrote to P.S. Miller, Howard says, "I am not sure that the adventure chronicled in 'Rogues in the House' occured in Zamora. The presence of opposing faction of politics would seem to indicate otherwise, since Zamora was an absolute despotism where differing political opinions were not tolerated. I am of the opinion that the city was one of the small city-states lying just west of Zamora, and into which Conan had wandered after leaving Zamora."
Although that does not indicate Corinthia by name, L. Sprague de Camp decided that is where it happened at, possibly because of the mention of the god Anu, which is probably Shemitish. It could have happened in Brythunia, which makes Anu an unlikely god, or a nameless city-state between Corinthia and Zamora, of course. However, that is the clue.