"Tell the Truth!" is not actually a game. It is a performance piece where Doug (imitating Will Smith's character from the movie "Concussion") asks the contestants for their favorite Will Smith movie. When the contestant answers, Doug, quoting a line from the aforementioned movie, yells at the contestant "Tell the Truth!" and then moves on to the next contestant and asks the same question. This continues until all the contestants have been yelled at.
The "Tell the Truth!" game has no bearing on the rest of the games. It's just comedy.