Jamie Diamon in his interview in Stanford said “ if I allow spinning to the public, you are going to spin to me” I found spin meaning as confused and several other meanings but I am not sure what does spinning means in this context
Oxford have the defintion:
spin (something) to present information or a situation in a particular way, especially one that makes you or your ideas seem good.
"Spinning" involves deceit. It is something that politicians do when they want to claim some fact is actually good for them, even when it is not.
Diamon is suggesting that if he allows (the people who work for him) to present information in a deliberately deceptive or self-serving way, then he won't be able to trust the information that he gets.
He is therefore claiming that information that comes from his organisations is not "spun" and is direct, straightforward and trustworthy.
The meaning comes from "putting spin on a ball so it bounces in a particular direction" (a cricket or baseball metaphor)