If you have evidence to back up that statement, please present it. This round, all evidence currently points to this being a simple BGA failure, not a failure of the in-chip solder bumps or other in-chip failures as you seem to believe.
Did you even read my post? I give you the most basic method to prove it's not the lead free solder balls. Heat the chip to 120c for five minutes- this is almost 100c below what you need to melt lead free solder. It brings the chip back for a short period.
For a more long term experiment - open a repair shop. Invest 10k+ into BGA rework equipment. When the failure occurs, reball the chips with leaded solder. For other customers, replace the chip with a new one. Keep track of who got a reball, and who got a new chip in the ticketing system. Then, compare the rate of people who come back, and keep track of who got a reball, and who got a new chip. If the answer isn't obvious inside of six months, you don't have a client base.
Our repair shop has had about 30 tickets per day, many being board repair, over the past three years. New York City is one of the top Mac places in the world in terms of population density of people with Macbooks over other brands, and people using them for artistic(read: CPU & GPU intensive) tasks. Give video editors reballed GPUs and watch what happens, it's not pretty.
My test makes it obvious it is not the lead free balls at issue. Any amount of research on flip chip design & failure makes that obvious as well, but if all of this is to be ignored, then try simple real world experience. It's fairly obvious to anyone who does this for a living what the answers are, and when you see all the reball shops with 30 day warranties closing after all the bad reviews and chargebacks and angry customers sink them, it really does become obvious.
I don't know who doesn't "believe" that these failures are internal to the GPU. Again, just mess & uneducated rumor spread on forums. But for anyone who doesn't "believe" this, I have about 60 pounds of GPUs for you to reball. Make me an offer and I'll sell you them!
Read this as well to learn more on flip chip desgn.
http://www.chipscalereview.com/tech_monthly/csrtm-1213-front.php