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Inverter and charger are two drastically different devices. An inverter doesn't do any voltage conversion, it's just PWM-ing the input voltage. A charger is a full-blown step-up/step-down converter with a dedicated transformer. I can imagine, that an inverter can be used as a charger in some limited cases, but its input/output voltage range is going to be very restricted and efficiency is going to be poor.
Brian provided a more elaborate answer to this, but basically AC or BLDC inverters are typically bi-directional. During regenerative breaking they're effectively acting as rectifiers, converting 3-phase AC input from the motor to DC suitable for charging the battery. While they may not directly control the voltage, they can control the current and thus indirectly control the voltage.
 

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Sorry, but what is the principal difference (electrically-wise) between brushed and brushless inverter except for the 3-rd half bridge?
As it gets to the charging, there are 2 main problems:
1) You get 240V in the outlet (345V DC). How on Earth are you going to step up that voltage to 420V in order to charge a 400V battery pack using, basically, 3 half-bridges? What to do with 120V (level 1) charging?
2) Since you cannot really regulate the voltage, only the duty cycle of the PWM. You have to skip a part of a sine wave in order to bring voltage down, just like a dimmer switch. The power factor of such system is going to be a disaster, no regulation authority ever would approve that for customer use. There is a reason why there is a switching transformer inside your phone charger and not just a PWM-ing transistor bridge.
I agree with you that stepping up voltage is probably one of the main issues here, when the charging AC input is significantly lower than what the battery pack requires. At the same time, here is what a trivial boost converter looks like :
and the inverter already has the MOSFETs or IGBTs for controlling the phases and current.
 
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