Reading about the Gunslinger on d20pfsrd.com
It is a move action to load a one-handed or two-handed advanced firearm to its full capacity.
Alchemical cartridges make loading a firearm easier, reducing the time to load a firearm by one step (a full-round action becomes a standard action, a standard action becomes a move action, and a move action becomes a free action), but they tend to be unstable.
Metal Cartridges used in Advanced Firearms seems to be listed in the Alchemical Cartridges table which would seem to imply that they are Alchemical Cartridges and hence that they invoke Rule 2.
I've found nothing that states that Rule 2 does work with Advanced Firearms.
This would imply that the Metal Cartridges reduces (Rule 2) the Advanced Firearms move action (Rule 1) to a free action as default. Am I missing something?
Not quite. Advanced firearms by default use metal cartridges, that's why the reload time is a move action regardless of the ammo used.