I agree with JohnW to a point. Granted, if the drive current limit were set correctly the current to the motor would be limited and the motor wouldn't burn out. But JohnW's point is only an issue if the drive is set up in specific ways or the motor is too small for the mechanical load.
If the drive is set up in V/Hz mode without any of the offsets voltages or custom profiles active then the motor will draw current from the drive 'similar' to what the motor does across the line. If the drive is configured with start boost or run boost voltages these can cause high currents if not set up correctly.
Also, if the drive is set up in one of the vector modes, either sensorless or with a sensor, the drive will try to develop a specific level of rotor flux. If the drive is configured to run a larger motor than it is connected to the rotor flux generating current alone, which is often 40% - 60% of nameplate current, will be driven through the motor regardless of load.
The fact that the drive can operate a larger motor without a problem leads me to believe that it is set up in a vector mode and, as JohnW said, it is set up for a motor larger than the one connected to it.
Keith