"This well-known problem has virtually no documentation on Internet forums... " - Honestly, just think how ridiculous this sounds.
Take for example a simple voltage divider with two resistors .... IN SERIES . Your telling me, that if I happen to NOT connect the center tap to anything in my circuit that one or both of the resistors in the divider will fail because they are connected in series? - That's essentially what everyone is claiming ... that's hog wash !!!
Take a step back please and objectively look at the content of the thread.
“that is essentially what everybody is claiming” Well, no, in fact that is not what everybody is claiming.
I know this is a lengthy response that might exceed the attention span of some folks, but I hope that you (based on that quite cool discussion of reversing SCL and SDA to avoid addressing issues [after several head pounding hours, I can’t see why it would not work in at least some instances]) will take the time to read it all.
The OP is reporting experiences of failures in series resistors in a particular product.
Nigel is reporting that such failures (in series resistors) are a common based on his considerable experience repairing a variety of products. This is his observation. IOW he has seen that problem many times – there are several resistors in series and that is where the failure has occurred.
I have no reason to doubt the veracity of both claims. Neither would have any reason to make it up and both would have the experience, in one case specifically, and in the other more generally.
Particularly notable is the additional information that when the multiple series resistors were exchanged with a single and higher wattage resistor (relative to the wattage's of the individual series resistors), and the problem was fixed and did not recur.
One of several possible reasons that multiple series resistors could be used rather than a single resistor is so that one could use lower wattage parts. There is agreement on this, both in the thread and in many other places. Not to say that there are no other reasons.
If one assumes the same likelihood of a resistor being outside of the rated wattage is the same or similar in the relevant cases, than the likelihood of a failure using three series resistors because it is out of tolerance is 3 times that of using a single resistor. Since a product failure occurs in both instances (in general), that analysis alone can explain the phenomenon. No ethereal, faith-based, explanations need be invoked.
Rated wattage is only one characteristic of the resistor and rated voltage is also applicable as well as time and heat-based long-term changes. The difference in likelihood of these characteristics could also follow the multiple, with regard to probability, as described earlier.
The number of products containing multiple resistors in series vs. a single resistor is not given. No claim regarding the percentage of failures in the series case vs. the single case is made and need be speculated, because a very low percentage can easily be consistent with the observations.
Obviously, the operating characteristics of the circuit relative to the tolerances of the resistors are a critical factor.
The OP is puzzled as he does not see operating characteristics close to tolerance. But, it is a small sample and there has already been a failure and the deviations in tolerance of the resistors has not been determined (and cannot be determined in the case of the failed ones).
Nigel’s anecdotal reports also do not include a comprehensive discussion of each circuit’s performance in this regard. I would not expect them to. Even a novice like myself can understand that cases exist with particular products having particular flaws that are revealed post-production. The idea that “everyone” might know this is completely understandable if you qualify the “everyone” as being those individuals who do the repair work.
Your simple resistor divider example could, in fact, demonstrate precisely the same phenomena, but you would need to replicate the experiment many times and know something specific about the tolerances and their deviations.
Finally, I acknowledge that Nigel (in post #37) suggested, what I believe to be, the same idea I am presenting here, but in a much briefer form.