There is a nice write up on this in the guides section. You can kill wanted ships of the system controlling faction with impunity. You actually get a bonus to your rep. Kill any wanted ship of any other faction in the system and you will get a hit to your reputation with that faction. Even if they fired first (that last bit annoys me somewhat).
- System authority has nothing to do with it.
- You lose no reputation upon kill if the ship had a bounty from its own faction. Which is always the case when it is locally wanted and belongs to system authority as well, hence the misconception, but it is not limited to system authority ships.
- Since the game does never tell you where the additional bounties revealed by the KWS are from, it is a pure gamble to attack wanted ships not belonging to the system owner.
- But by extension that means if there are no extra bounties, you are guaranteed to lose rep with the faction if it isn't the local authority.
I hope FD will add some indicator to the HUD whether the ship has a bounty from its faction, like a the word "WANTED" after the faction name; of course this would only apply when you have performed a kill warrant scan.