I've read this several times now and it's pretty much wrong.
An electronic ompass works with 2 (or sometimes 3) magnetometers. So it can detect a magnetic field along two or three axes.
See e.g. this device:
The two 8 pin chips on theleft and below are two magnetometers. And one is placed 90 degrees to the other to be able to measure two axes.
Now these two magnetometers output voltages in return to the magnetic field applied. Due to metal parts in the remaining device and due to limited absolute accuracy of such devices, you cannot determine the exact heading just from these two values. But once the device has been rotated and the CPU monitoring it has seen e.g. the max values returned by the magnetometers when each of them pointed exactly north/south, then the CPU is able to calculate the heading quite precise.
However, if the device is switched off, it usually looses the calibration data. Also after some time the sensors behavior may change as different battery voltage levels may cause different megnetic fields to be generated by other parts in your device etc etc ...
So it's not because they are supplying unregulated battery power directly to the chip.