In this situation, it is Chuck Norris, not the person starting the conversation, who actually comes up with good ideas.
In this situation, it is not the person starting the conversation who comes up with good ideas, but the other person (in this case, Chuck Norris).
Edit: Sorry, I should have said that yours was correct. I just find the opening thirteen words rather wordy and potentially confusing. I'm a little uncomfortable with "... it is the person other than the one starting the conversation ..." but I can't quite put my finger on why.
Student or Learner