This is nothing but a guess, but I think they over-promised on performance and current battery technology couldn't deliver.
If it's a flawed battery, you replace it with a proper one. Fine, done. I'd be floored if there was a charge controller logic problem that couldn't be fixed in software. They're either using an industry standard power management chip that's got millions of units worth of field testing or they've implemented it in their own SoC. If the former, the logic is solid and tested. There's some switches they can flip to control its parameters, but those are all pushed over from the SoC via whatever low-level driver package they wrote. Field updatable. If they implemented it all in the SoC, they should be able to fix it, also with a firmware update.
My guess is that they promised battery life claims that they couldn't fit into the phone with current best battery technology. They're pushing the limits of the lithium they could fit into their package and either over charging it to push that last bit of capacity into it, over-drawing and discharging it too quickly, over discharging it, or some other combination of power levels that are too much for *any* battery that would fit into the space they have to work with. They *could* make the phones stop burning if they tuned the power management to more conservative levels, but then they'd miss on battery life promises and probably be stuck with recalls or class actions based on false marketing.
It sounds like they may have tried to switch to a battery that could offer a *little* more and maybe tweaked the PMC settings as much as they could and still meet their battery claims, but it fell short in at least some devices / usage scenarios. Maybe they're getting some number of batteries that can't be stressed quite as hard as they're pushing them. Maybe certain usage profiles put more stress on the batteries, and only certain users are pushing it enough for the new combination to be dangerous. Either way, it sounds like marketing promised what engineering couldn't (safely) provide, and they're screwed. I'd think the only valid choices would be to redesign the phone to require less power or to make more room in the enclosure to include a higher capacity battery that wouldn't have to be run so close to red line to meet the phone's power requirements. Either way, not something they can do and get to market in a recall timeline. Pulling the plug until they can reengineer is the only option.