Yes, he didn't tell anyone, but he didn't tell them because he didn't want them to be swayed by production, which may not have been the best move, but the fact is since Cody dared to put Paul on the block, Paul became obsessed with getting Cody out. The others went to Paul more because he had safety for 3 weeks than the fact Cody lied. That is my opinion, I don't know for sure, but something tells me if Paul only had safety for that 1 week, Cody's alliance probably wouldn't have turned on him. Christmas also became obsessed with the fact he put her on. She never once considered that Cody was put on the spot and just had to come up with a name within seconds. I think at that point Christmas was the closest to Paul and Cody just went with her. I think if Cody had a little more time to think it over he wouldn't have picked her and would have picked someone like Rames or even Kevin who was not in his alliance. It is what it is and that's mostly because of production's interference, but whatever I continue to watch for some reason, I guess they are doing something right lol.
Edited to add I also believe if Paul had not been safe, everyone in Cody's alliance would have been just fine with him leaving them out of the loop they might have complained a little, but at the end of the day they would have forgave him, JMHO again, but I do believe that.