I ran into this too in a LAN game with both of us allied against 2 AI's. It got very strange, in that some of the planets we each had colonized thwe other one of us saw as still being controlled by the enemy or neutral.
Also I had eliminated the pirate base entirely with it registered as dead (complete with shattered glass and 0:00 opn the pirate bounty screen.) Hopwever for her the pirate base was still registered as intact, complete with bounties and randomly sending out pirate waves only she could see. (which attacked and blew up planets I had colonized, but once against only registered this on her game.)
In the end it displayed a "victory" screen only for me, making her wipe out one of the enemy colonies that only registered for her before gigiving her the victory screen.
(I have the save and replays if anyone needs them)
Edit: oh and we were still networked as we coudl freely transfer resources to one another via the trade screen