Yes this error is caused by a break in a solder ball underneath the GPU. 0102 definitely has a good chance of being repaired, despite previous attempts or board flexing. But it is not going to be fixed with thermal paste or tightening the bolts. All tightening the bolts does is put pressure on the chip to just make the two separated points meet again. This can ruin the chip over time and if it breaks again, a full reball or a whole new GPU may be needed to repair it.
The cracked solder joints are caused by rapid heating and cooling of the solder. Because the solder is lead free (because I believe any product marketed towards children in the U.S. has to be free of lead), the solder becomes very brittle and cracks.
You'll need to get it reflowed or reballed by someone with a reworking station. Reflowing is when someone cleans under the chip with flux to remove oxidation and purify the solder, then they use a reworking station to remelt the existing solder on the chip, bridging any cracked points back together. A good solid reflow can last years if done right, but it depends on the Xbox.
A reball is when a reworking station is used to melt the solder, then the whole chip is removed, the solder is cleaned off, and new solder balls are placed back on using a reballing jig. Reballs are the best solution because when the balls are replaced, leaded solder is often used, which is much more resistant to rapid changes in heat.
There are many companies and individuals with the tools for this on this forum and many others. I have the know-how and materials to perform a reflow for you, but I do not yet have a reballing jig for a reball. Reballs are usually pretty pricey though, considering the time and patience that goes into them, so I think your best bet would be to have it reflowed.
I usually charge between 20-25 dollars for a reflow, not including shipping. And if I deem the board irreparable, shipping is all that is charged.
Also, you will find MANY youtube videos on reflowing with a "heat gun." Many people swear by it, but I advise against it. The airflow is not even or temperature controlled like a reworking station, so surface components can be blown off, capacitors ruptured, I've even seen a RAM chip blow off and hit a guy in the face when he was trying to heatgun one. Plus, you will likely warp the board because of localized thermal expansion.
Good luck!