I think the problem lies in making the batteries too dense and then using quick charging technology. Quick charging will charge the phone to 60% in 15 minutes. . . but it does it with a lot of heat being added and the battery will expand. Do that to a Lithium Ion battery that has some already existing internal connectivity issues, and you are likely to get discharge arcing inside. That may result in more and more arcing as the charging cycles repeat. Eventually that results in a fire.
Of course, damaging the battery by putting too much pressure on the battery in assembly can exacerbate that as well.
Apple has eschewed the fast charging cycle, although they certainly know the technology and could incorporate it in their devices, I think for that reason. Trickle charging does not heat the battery anywhere nearly as much.
I think you nailed the crux of the issue. The fast charge may enable an acceleration of the failure mechanism. Apple has, for its own reasons, placed multiple charge regulation circuits between the storage media and the Lightning port or the circuits that utilize the power.
Perhaps Apple has done more extensive testing - which I believe would have exposed this issue long before the Note 7 launch. It is my opinion that either Samsung failed to do product testing, or ignored a result they did not like. Apple has postponed a product launch multiple times and not elaborating as to why. Perhaps Samsung was too set to meet or beat Apples iPhone 7 launch and made a serious error in releasing a product that should never have been launched. Apple has never had a similar catestrophic launch.
I have high expectations for the SolidEnergy solution.