Apologies but I missed this article:
Common ground and why you need one
and it reminded me that current always returns to the source. So even if the 12V ground is connected to a ground pin on the arduino and the emitter of the BJT is also connected the to same ground pin, the current from the 12V circuit will flow back to the battery and not through the arduino, I think.
Where the negative of the LEDs is connected to the emitter of the BJT, that allows the current in the 12V circuit, which is diverted from the mosfet to ground via the BJT, to flow back to the battery and not the arduino. The current from the BJT emitter flows back to the arduino and not the battery.