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The origin of this myth was that charging a lithium ion battery while using it could cause the battery to explode, however this would only happen when using third-party chargers.
They were cheaply designed and can cause over-voltage, resulting in the battery overheating and potentially exploding, or simply damaging the lithium.
These days however, most chargers, third-party or otherwise, are much better designed and will allow simultaneous charging and discharging just fine.
This is also related to the myths of letting your battery die before charging, which will actually CAUSE damage, and not letting the battery charge over long periods, which is simply not true.
In summary, charge as often and as long as you can, as long as you power it down from time to time.