I'm from Bilston, and you're right that Wolverhampton was not considered to be a part of the Black country but now claims to be the Capital of the Black country much to the Chagrin of Black country locals, Bilston is always being tied in with Wolverhampton Bilston Folk Hate this.
The saying Black in the Day and Red at night actually comes from the foundries that stretched all the way from Dudley through Tipton Coseley Bilston and Wednesbury the Biggest Foundry being the Spring vale Foundry in Bilston nicknamed Big Lizzy on dark winter night when I was a lad you could really see that thing glow Bright red in the dark and in my eyes looked quite beautiful, in fact when the Foundry was closed ad blown up in 1980 I found it quite difficult to sleep with out the clanging of the steam hammers and the coming and going of the coal trains. There are lots of legends as to why its called the Black country,the Black in the Day red at night was always a popular saying around here in the heavy industrial period, a more amusing tale is that when Queen Victoria passed through here on a visit she glanced through the window of her coach complained that every thing was so dark and black with smoke she closed the curtains so the view didn't offend her.