Well put David! I think you are right and I would prefer your response.
It means ..... when I say something or state something, I know for a fact that it is true because I have proof (traigo los pelos en la mano). This saying was used many, many years ago in Mexico. I work with elderly people and I have learned so much..... culture, language, idioms/sayings, etc.
Thank you for giving me the opportunity to explain this particular saying that I thought was so funny when I first learned it.
Eliana