Ever tell a story the second, third, or even fourth time and not remember exactly what you told the other groups you told it to? It's kind of like the fish story. The fish gets bigger every time we tell it.
If we consistently tell the truth, we can tell it over and over again as what is true doesn't change. When we embellish it or modify it in order to make ourselves look better or keep ourselves out of trouble, we, usually can't remember the modifications so we tend to tell the story differently each time we tell it. Over time it may not even look like the same story.
Mark Twain's thought is simple: Tell the truth and you won't need to remember which story you told to which people.