Interesting - I thought that the 8xxx series was especially prone to having issues, to the point that NVIDIA released a revised version with different underfill for the die. Not sure why they would have bothered doing that if the problem were indeed the solder balls connecting to the motherboard?
I'd never heard of universal GPU-specific solder ball defects in this timeframe, so I looked around a bit and found this video from acerbic repairman Louis Rossman:
His thesis, from having worked on a wide range of hardware, is that premature GPU deaths are mostly due to the flip-chip die ball bumps warping off the interposer. He says this is why heating up to 140º (a la
@bobesch) appears to work - it warps the die back so it contacts the interposer again for a while, until it heats up and fails again. (If the problem were instead with the solder balls themselves, heating up to 140º shouldn't do anything at all since, as you've said, the melting point of solder much higher.)
He of course recommends full chip replacement when parts can be found, though he also expresses the regrettable opinion that legacy Macs aren't worth fixing...
So I think that it is possible that a wide range of GPUs would exhibit flip-chip bump problems due to being run in thermally-constrained environments and overheating. As Rossman says, reballing can help temporarily, and the issue may not always return in well-ventilated or low-demand environments. Probably worth trying in some cases, especially when replacement chips are prohibitively expensive.