Pi tells the "real" story at last. Why do Mr. Okamoto and Mr. Chiba ultimately report Pi's original story-with animals-instead?
Pi shows Mr. Okamoto and Mr. Chiba that the "real" story, the one with his mother, the cook and a sailor, is only one version, and it is a flat, immobile version. It conforms nicely to their world view. In other words, even if it is an exact objective account, this version does not lead to new knowledge, new insights about existence, survival, science or spirituality. It is a scientific formula for what happened.
For example, to say someone is the light of your life is not a scientific statement about the world. Unless, of course, you live on the dark side of the moon and your significant other owns a flashlight. Kidding aside, this phrase means that you are feel 'brighter' and 'more alive' when this other person is near; the metaphor is true. Metaphor expresses truth in ways that science does not. Discussing the complex firing of neurons resulting in the cognition of love and its reciprocating rise in blood pressure is a flat, immobile way of describing how the light of your life 'raises your spirit.'
In this case, the story-with-animals is more interesting. Just as important, it may also help you understand the experience more, or differently and thereby, it adds truth to the 'facts.'
In the end, Pi is trying to spiritually enlighten his inquisitors by showing them that, in terms of truth, there is no difference between the two stories. The two stories are different ways of understanding. And if Pi used this story to get through this ordeal, who's to say that his experience of using this story-with-animals in this way is not true? Because, isn't the "real" story also a story?