Unfortunately, that analogy just doesn't work in the car industry. People will still buy the BMW because it is a BMW.
To back it up, I'll give you a two real world examples, both to do with another car Manufacturer - Porsche.
When Dr Ferdinand Porsche first created his company, his Porsche 64 was created using many parts from the VW Beetle.
From my personal experience, back in 2002, I was helping my brother strip down his 1986 Porsche 944 turbo to be raced in 03.
While pulling the car down, I noticed that many of the parts were manufactured by Audi and VW (which admittedly owns Audi). Even while we were stripping the sound proofing material off the body, I found out that the body of the car was manufactured by Audi, which to me was very surprising (given the body was one of the main selling points of the car at the time, even Mazda ripped off the design for the RX7).
If I had to give a rough breakdown in parts, I would have said that particular model was a 3-way split when it came to who's parts were in the car.
As for Porsche's company performance, they are one of the strongest car brands worldwide and definitely one of the most profitable, in 07 having made 5.8 Billion Euro profit off of 7.3 Billion Euro in revenue.
Currently, the only thing that is causing them headaches is their financial acrobatics, not the fact that their cars are made out of other manufacturer's parts.
So unfortunately, your analogy just doesn't hold up.