Wait, wait, wait… Are they saying that if the battery is too drained the device will not charge? It that’s the case, it’s a terrible design decision!
Also, isn’t the + shaped control a Nintendo patent?
Secondly, did you even read past that paragraph? They got a new supplier and replaced the batteries with better ones in every device.
Their write up seems to imply that the device wouldn’t charge if the battery is completely drained.
It happens sometimes in cheap devices in which the charging logic is managed in software, but it’s a terrible design decision.
If that’s the case, a better battery will mitigate the problem but the terrible design remains!
In my experience, this is a pretty common practice, not limited to cheap devices. Many modern battery-driven devices I've looked at closely (for example: e-book readers, smartphones, ...) cannot bootstrap from a completely dead battery. They have to bring up the CPU, which then brings up the PMIC, before it can start charging the battery.
The difference between well-designed and less well-designed devices is mostly in how well they protect the battery from discharging beyond the point where this minimal bootstrap process stops working.