Glamdring What you've described is counter to what @pajada said in his reply to my question. He confirmed my statement that "the AI bot player will be placed last in all games they play no matter their Culture score." I declared a huge War on Culture against another player (instead of the AI Bot, who is currently in first place) based on Pajada's response, so I hope he was telling the truth!
I believe that the reason you see yourself getting Tournament Points for a 3rd place finish (instead of a 2nd place finish) is due to the following passage in the Tournament Rules:
Every player who runs out of time will be placed last with score 0 points independently of the score of AI who replaced them.
This will not be reflected directly on this web, final standings will be done in Google Docs manually (link comming soon).
So, I think it is simply that the CGE Tournament System does not display the score in the manner that Pajada has described the tournament rules. In your specific example, Pajada will be giving you points for a 2nd place finish on his Google Docs, even if it's not reflected on the CGE Tournament System.