There are thousands of people that fix this problem - and if paperclips are involved, then it's not a good fix. The processor isn't touching anything that it shouldn't be, the motherboard warps underneath the GPU, and the (cheap) lead-free solder breaks. Some people have "fixed" this by sticking pieces of tooth picks (or paper clips I suppose) under the bolts that go in the X-Clamps (which hold the heatsinks in place), which causes the heatsink in turn to put more downward force on teh GPU, bridging the connection. It's a pretty crappy fix, though it is effective, at least sometimes, and almost always it's short term. While you can say if the system ran cooler these problems would not happen - and that's technically true, but it's not because of the system overheating, it's because the crappy design and the cheap lead-free solder can't handle the heat that actually is produced.
Here are some pictures of the cooling mods I've done to my 360, just to show that I'm not talking out of my ass. I've also done the X-Clamps replacement, replaced the thermal paste with Arctic Silver 5, and reflowed my GPU's cold solder joints with a 1000 degree heat gun.
http://forums.xbox-scene.com/index.php?showtopic=636737