No, I don’t know why this trailer is called Cherished Memory. I do know that it involves a guy in a cowboy getup shooting a guy in a costume into the air with a shotgun. Then he makes an obscene gesture. It could be a cherished memory.
It does illustrate some of the ridiculous things that you can in Saints Row: The Third.
Look for this and more crazy things in Saints Row: The Third on November 15th, 2011 for PC, Xbox 360, and Playstation 3.