I just checked: tiny suicidal game, 9 AIs, cheats enabled. I revealed the map and checked homeworlds with my spy. A half of them had already 2 buildings BUILT, another half had 1 building built and another one in queue. Those with 2 finished buildings had the third building finished after I pressed the Turn button for the first time. To repeat again: they had 3 finished buildings besides starting Civ capital and Starport in the second turn.
I had to check another suspiction. I saved the game turn 2, and immediately loaded it gain. Guess what? When the turn was loading, I got the message that the Torians built manuf capital (that wasn't in the queue), and the Entertainment Network, that was in queue on their HW before saving, was BUILT! I saved the game again (still the second turn!), and loaded it. This time Iconians built the Manuf. capital, and most races had built the queued building.
So AI doesn't get just a free diplomacy turn after the game is loaded / started, they also get a free production turn. Every time! ...
BR, Iztok
Maybe I'm just obtuse, but I still don't see any evidence of an extra round of diplomacy here. No one before this reply (10) had mentioned free diplomacy, either. As far as I can see, you just assumed that it was the case, but your investigation doesn't seem to have been able to show that. I wonder if a debug would show it, if the AI had extra trades.
Either way, free diplomacy would probably not be nearly as big a deal as the free planning/rush-buying that we know the AI gets, and I'm not even much worried about that.