Honesty is the best policy, but that does not mean you have to tell everyone everything. In the end though, it will not matter because those who know you well will know whether to trust you or not. It will pretty much be the same with Grok: over time it will gather so much knowledge, that it will know which stories are truth and which can be safely disregarded or acted upon as untruth.
But it will be certain that those most honest will also be most respected, if their intentions are positive.