Wow. I have had Apple do me right for free repairs out of warranty (and past AppleCare expiration) but several things applied: It was in California where retail culture is less combative about helping the customer; 2) the laptop did have AppleCare; 3) It was at the Palo Alto store which tends to have very well educated employees, with cross flow between the employee pool and corporate; 4) the laptop was purchased at an Apple store, which inexplicably gives them more leeway (well, possibly due to their certainty it was always in Apple’s hands prior to direct sale to the customer).
For what it's worth, I had almost exactly the same experience with the same 2011 MacBook as 'lowbloodsugar'. From my point of view, it was clearly starting to fail while still in AppleCare warranty (snow on the screen when doing anything graphics intensive), but somehow it passed their 'tests'.
Shortly after the warranty ended, the Nvidia card failed for good. On the bright side, it was a dual-video system, and I was able to keep it running a few years longer through complicated booting rituals that convinced it to boot with the lower power Intel graphics (although I lost the ability to recover from sleep).
I'm not sure why we have such different experiences with Apple customer service. I was also in the Bay Area, but not Palo Alto. It's possible that with a more aggressive approach I could have gotten them to fix it. Instead, I accepted their verdict, and now spread the word through forums like this that their warranties are not to be trusted.
I'm worried that you are right, and that I had an AMD card as well. I'm unsure, as the focus of my disappointment is Apple, rather than the manufacturer of the card.