In Italy washing the coffee pot with detergent is considered a sin.
The "oily" that you describe gives a better taste, and it's something that every "nonna"(grandmother) teaches you, if you want to clean your coffee pot just put it under hot water and brush it with your fingers, that's it.
Source: I'm from the south of Italy, and I have Nonnas :D
Source: I'm from the south of Italy, and I have Nonnas :D