The original black paint cameras belong to the correct serial number blocks. They were prepared in the factory with the intention of being black painted. For example, chrome thickness differs from black paint thickness. There has to be minute adjustments to make sure that black paint camera parts don't rub in use, for example.
Usually, people don't decide to turn their perfectly excellent to mint chrome camera into a black paint one. They usually use a beat up camera to start with, knock the dents out, and acid remove the scratched up chrome. You hope that they will do an overhaul on the interior parts while they're at it. In the end, it may outwardly look beautiful, but it's got the counterfeit feeling. The only time it would be honest is if you repainted a black paint camera into new black paint. But then, you have severely devalued the collector value by scrubbing off the original paint and patina. So, nobody does that.
The serial number for your counterfeit camera will be wrong for black paint.
It's as authentic as a "gold Kriegsmarine Leica IIIc with swastika insignia" that somehow miraculously looks mint having survived World War II, and kind of resembles a FED.
All the difference in the world: real black paint vs a repaint.
One is an elegantly aged, but still beautiful lady.
The other one is a tarted up cheap whore full of hidden diseases.
