To pull 300 amps when starting an engine it must be the live connection to the starter motor , it is direct ( always live) the solenoid makes the circuit, from my experience starting cold was fine it was hot starting that was getting difficult, I did not blow a fuse but would have if I kept trying to turn the engine, BMW have had a recall notice on the B58 engine to replace the starter motor with this very problem and advised to park outside as it could result in a fire.
