I would strongly discourage anyone from making things up. I have participated in these exercises, and many people simply said, “I really have nothing to share that would interest you.” Those were the people others respected the most.
They might share personal things with close friends, but they had a clear definition of what friendship meant.
In other words, be a person of character.
It is perfectly fine not to be friends with everyone. Just be respectful and honest. Do not lie. Say, “I cannot tell you that because of this or that,” or simply remain silent.
The problem is that responding that way could be seen as anti-social and counter to the cultural identity of the organization.
Companies will use everything and anything against you when they believe it’s time for you to go.