Thank you for the followup. The quoted passage is correct, but was not part of AEG’s original printed rules nor the current PBE rules (Which currently do not support multiplayer - look for that update soon). I’ll repeat here for clarity:
Effects that refer to “your posse” can only be played by either the leader or the mark i.e. the players who have a posse. >Third party players do not have a posse and so cannot play such cards.
To answer the OP: The Leader/Mark controls the shooter and thus a third-party can NOT play Outgunned or other cards that refer to ‘your posse’ or ‘your shooter.’