Mac,
The idea of taking a Ferrari and 'diluting' it to produce a FIAT - what great thinking!
Many different manufacturers produce a 'budget' brand as a spin-off of their premium product... my mind is brimming with examples as I write this, e.g. Karcher waterblasters/Karcher 'Cip', Continental Tyres/Barum, Clarion car audio/Addzest, Smeg/Classique (kitchen appliances)...
Usually the reason is that they want to compete with lower-priced competition without the risk of harming the reputation/resale value of the premium brand.
Sometimes, manufacturers even seem to have gone the other way - taken a low-end product and offered it under the 'premium' brand - remember the Porsche 924? And of course, there is the example of Lexus: Toyota didn't want to use their own name.
But I think there is plenty of scope to take a Ferrari, replace the components with cheap FIAT items (hell, most of the switchgear is probably FIAT already!), make the body a little cheaper to produce by cutting a few style corners here and there (like the plastic side intakes of the X1/9 compared with the Ferrari 308!) and stick a FIAT badge on it.
I'd be happy, I think you would be happy, and Ferrari customers would certainly not be worried...
-Alex