Poirot vs Columbo

There's an episode of Columbo, "Dagger in The Mind" I think it's called, where Columbo visits Scotland Yard, and is attached to a Chief Inspector of Detectives, and largely seeming to defer to him, while gently prodding him with questions and problems he has with the investigation as it proceeds, such as a valuable book being laid down in a way that could damage it. I feel Columbo would use a similar tact with Poirot, and of course mistake him for French and go on a long winded apology and story on being corrected that he is Belgian, possibly insulting his culture mentioning waffles.