Well yes, the battery may be at the root of the problem for these phones as they've indicated, however ANY LiPo battery will catch fire if poked or ripped open like that. Lithium is a volatile metal and by it's very nature is dangerous.
Like all very alkaline metals, Lithium is highly reacting and flammable. In its raw form it's stored in oil prevent it from reacting with Oxygen in air and bursting into flames. By puncturing them or unwrapping them as in the video, you're essentially exposing the Lithium to Oxygen and starting the reaction which is then self-sufficient and will continue to burn until all Lithium has been oxidized. If contained in a small space it will reach extremely high temperatures and can be explosive if contained under pressure.
These LiPo batteries are really being used within a very narrow "safe zone" of operation and both the discharge and charge rates, along with internal temperatures have to be monitored very closely in order to prevent them from self-destructing.
There are very complicated circuitry systems and algorithms incorporated into the phones and also inside the batteries themselves in order to keep them operating safely as possible. The charging adapters are NOT intelligent most cases (except for the new Rapid Charging adapters), and instead simply supply the stepped down and regulated DC voltages necessary to activate the charging circuitry. It's the phone and battery that do all the charging and monitoring to make sure the batteries remain safe. Just one flaw in any of these safeguards can result in these batteries becoming incendiary devices. This is most often the cause self-destructing (thermal runaway).
If the circuit on the board internal to the phone fails, the one in the battery is supposed to protect itself. If however the failure of the phone charging board is such that it's damaging the battery's protection board then the battery will suffer extreme charging and this will result in it burning up.
So what I'm saying is the video itself doesn't prove their batteries are any more dangerous than others when used normally.
Ref:
Lithium - Wikipedia, the free encyclopedia
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