That's not hot enough to melt lead, tin, or anything else. The only way that such a small temperature increase could make any difference at all is if the additional heat causes enough thermal expansion to bring a broken bit of metal back together. That's far more likely to indicate a broken solder joint somewhere than anything else.
More importantly, that test provides no indication of whether that failed solder joint is inside the chip or under it, unless you've somehow found a miraculous way to heat up a chip without heating the solder joints underneath it, and without causing any thermal expansion of the outside of the chip's packaging.
I'm not saying that you are necessarily wrong—you could easily be correct—but nothing you have said qualifies as evidence, much less proof; it is all hearsay and anecdotes. A minimum standard of evidence for proving that the failure is internal to the chip would involve X-ray scans of an affected board, showing fractures in the chip where electrical conductivity is interrupted. Absent such evidence, statistics suggest that solder joints are the most likely culprit.
The fact that some reballers fail is a meaningless piece of information. There are lots of people who have had reballing jobs (done by people who know what they are doing) and
did not experience subsequent failures. Although we won't know with any real certainty whether reballing truly solved their problem until a few years have passed, the best evidence to date strongly suggests that the solder joints are the problem, and that reballing does fix that problem.
The reason the reballing shops you describe have failed is that doing reballing correctly is nontrivial, and it is far easier to do it wrong than to do it right. One critical difficulty with reballing is the need to remove every last trace of the existing solder. Otherwise, you get a weak spot where the two types of solder meet, and the result is a weak joint that fractures very easily.
Additionally, assuming that the reballing company also handles the rest of the repair job, if they don't know what they are doing, they'll screw up the heat sink installation, which can lead to a quick failure as well.
