The above poster is correct, I think the most relevant rules are the following 3 references all from page 11 of the rules:
Pirate Truce: NPC Pirate ships will no longer attack you
(see “Hunt Priority” on page 13).
Only mentions a restriction on NPC pirates and not on players
Example: You have just defeated a Pirate player
with 3 Bounties from Spain and 1 from England.
Claiming the 15 Gold reward from Spain would
be nice, but since you have a Bounty from Spain
yourself, you can only choose to claim the 5 Gold
reward from England.
This is a specific example of a pirate player getting paid for attacking another pirate player.
Defeating the Pirate Sloop earns
you 5 Gold and defeating the Pirate Frigate earns you
15 Gold. Only non-pirates can claim such a reward.
This is not as specific as the above reference for player pirates but the last sentence implies to me that a pirate can defeat a NPC pirate but may not claim the cash reward for doing so.