The pronunciation "dee-troit" is just local slang meant to sound folksy. It's used by sports announcers and singers, and for comedic value. Most of the time people in the area pronounce it the same way as the rest of the country pronounces it.
I think you're right there. But also going back, there was a more 'neutral' pronunciation of "deh-troit". I believe from there, we started getting "duh-troit" as a type of Schwa[1]. Again, I agree that there's a newer "DEE-troit" which is kind of like if you drew a line from "duh-troit" through "deh-troit" and kept going, then you'd get "DEE-troit".
